Mutually exclusive and independent events

There are only red counters, white counters, blue counters and green counters in a bag. Chris is going to take at random a counter from the bag. The table shows the probability that he will take a red counter and the probability that he will take a white counter.

There are twice as many blue counters as there are green counters in the bag.

Work out the probability that Chris will take a blue counter.

There are 45 red counters in the bag.

Work out the total number of counters in the bag.

There are only red counters, white counters, blue counters and green counters in a bag. Chris is going to take at random a counter from the bag. The table shows the probability that he will take a red counter and the probability that he will take a white counter.

There are twice as many blue counters as there are green counters in the bag.

Work out the probability that Chris will take a blue counter.

There are 45 red counters in the bag.

Work out the total number of counters in the bag.

Freya and Ria each do an exam. The probability that Freya will pass the exam is 0.8 The probability that Ria will pass the exam is 0.85

Complete the probability tree diagram.

Work out the probability that only one of Freya or Ria will pass the exam.

The table shows the probabilities that a biased dice will land on 3, on 4, on 5 and on 6

Karim assumes that the probabilities that the dice will land on 1 and on 2 are the same. Karim rolls the biased dice 500 times.

Assuming Karim is right, work out an estimate for the number of times the dice will land on 2

Karim is wrong. The probability that the dice will land on 2 is greater than the probability that the dice will land on 1

How does this information affect your answer to part (a)?

The table shows the probabilities that a biased dice will land on 3, on 4, on 5 and on 6

Karim assumes that the probabilities that the dice will land on 1 and on 2 are the same. Karim rolls the biased dice 500 times.

Assuming Karim is right, work out an estimate for the number of times the dice will land on 2

Karim is wrong. The probability that the dice will land on 2 is greater than the probability that the dice will land on 1

How does this information affect your answer to part (a)?

Dan is playing cards. The probability that he will win a game of cards is 0.3 Dan plays two games of cards.

Complete the probability tree diagram.

Work out the probability that Dan does not win either game.

Dan is playing cards. The probability that he will win a game of cards is 0.3 Dan plays two games of cards.

Complete the probability tree diagram.

Work out the probability that Dan does not win either game.

Tim has two biased coins, coin A and coin B. He is going to throw both coins. The probability that coin A will land on heads is 0.6 The probability that coin B will land on heads is 0.55

Complete the probability tree diagram.

Tim throws coin A once and he throws coin B once.

Work out the probability that both coins land on heads.

Tim has two biased coins, coin A and coin B. He is going to throw both coins. The probability that coin A will land on heads is 0.6 The probability that coin B will land on heads is 0.55

Complete the probability tree diagram.

Tim throws coin A once and he throws coin B once.

Work out the probability that both coins land on heads.

Shakir has to complete two tests. He can either pass or fail each test. The probability that he will pass the first test is 0.87 If he passes the first test the probability he will pass the second test is 0.94 If he fails the first test the probability he will pass the second test is 0.73

Complete the probability tree diagram for this information.

Work out the probability that Shakir passes at least one of the tests.

There are only blue pens and red pens in a box. The number of blue pens is four times the number of red pens. Rita takes at random one pen from the box. She records the colour of the pen and then replaces it in the box. Rita does this n times, where n 2 Write down an expression, in terms of n, for the probability that Rita gets a blue pen at least once and a red pen at least once.

Here is a 4-sided spinner.

Samina spins the spinner once.

Choose the word that best describes the probability that the spinner lands on 2

Choose the word that best describes the probability that the spinner lands on a

Ralph rolls a biased dice once. The probability that he gets the number 5 is 0.4

Work out the probability that Ralph does not get the number 5

There are only blue counters, green counters, red counters and yellow counters in a bag. The table shows the number of blue counters in the bag.

There is a total of 100 counters in the bag. Ashin takes at random a counter from the bag.

Find the probability that the counter is not blue.

The ratio of the number of blue counters to the number of green counters is 2: 3

Work out the number of green counters in the bag.

Bradley says, “The number of red counters in the bag is the same as the number of yellow counters in the bag.”

Can Bradley be correct? Give a reason for your answer.

One weekend the Keddie family is going to do a sports quiz and a music quiz. The probability that the family will win the sports quiz is 0.3 The probability that the family will win the music quiz is 0.35

Complete the probability tree diagram. Sports quiz Music quiz

Work out the probability that the Keddie family will win both the sports quiz and the music quiz.

One weekend the Keddie family is going to do a sports quiz and a music quiz. The probability that the family will win the sports quiz is 0.3 The probability that the family will win the music quiz is 0.35

Complete the probability tree diagram. Sports quiz Music quiz

Work out the probability that the Keddie family will win both the sports quiz and the music quiz.

There are only blue counters, red counters and green counters in a box. The probability that a counter taken at random from the box will be blue is 0.4 The ratio of the number of red counters to the number of green counters is 7: 8 Sameena takes at random a counter from the box. She records its colour and puts the counter back in the box. Sameena does this a total of 50 times. Work out an estimate for the number of times she takes a green counter.

There are 15 sweets in a jar. 4 of the sweets are red. Jill takes at random a sweet from the jar.

Write down the probability that the sweet is red.

There are only green counters and blue counters in a bag. A counter is taken at random from the bag. The probability that the counter is green is 0.3

Find the probability that the counter is blue.

Lorena gets a train at the same time each morning to go to work. She gets a train at the same time each evening to come home. The probability tree diagram shows the probabilities of each train arriving late.

Complete the probability tree diagram.

For a day that Lorena goes to work,

work out the probability that the train to work and the train home will both arrive late.

In a bag there are only red counters, blue counters, green counters and pink counters. A counter is going to be taken at random from the bag. The table shows the probabilities of taking a red counter or a blue counter.

The probability of taking a green counter is 0.2 more than the probability of taking a pink counter.

Complete the table.

There are 18 blue counters in the bag.

Work out the total number of counters in the bag.

In a bag there are only red counters, blue counters, green counters and pink counters. A counter is going to be taken at random from the bag. The table shows the probabilities of taking a red counter or a blue counter.

The probability of taking a green counter is 0.2 more than the probability of taking a pink counter.

Complete the table.

There are 18 blue counters in the bag.

Work out the total number of counters in the bag.

Pat throws a fair coin n times. Find an expression, in terms of n, for the probability that Pat gets at least 1 head and at least 1 tail.

Sally plays two games against Martin. In each game, Sally could win, draw or lose. In each game they play, the probability that Sally will win against Martin is 0.3 the probability that Sally will draw against Martin is 0.1 Work out the probability that Sally will win exactly one of the two games against Martin.

There are only 5 blue cards, 2 green cards and 4 red cards in a pack. Isabella is going to take at random one card from the pack.

Write down the probability that Isabella will take a blue card.

Ken is going to throw a biased dice once. The probability that the dice will land on six is 0.3

What is the probability that the dice will not land on six?

Amanda has two fair 3-sided spinners.

Amanda spins each spinner once.

Complete the probability tree diagram.

Work out the probability that Spinner A lands on 2 and Spinner B does not land on 2

Amanda has two fair 3-sided spinners.

Amanda spins each spinner once.

Complete the probability tree diagram.

Work out the probability that Spinner A lands on 2 and Spinner B does not land on 2

There are some counters in a bag. The counters are blue or green or red or yellow. The table shows the probabilities that a counter taken at random from the bag will be blue or will be green.

The probability that a counter taken at random from the bag will be red is five times the probability that the counter will be yellow. There are 300 counters in the bag. Work out the number of yellow counters in the bag.

In a bag there are only red counters, blue counters, green counters and yellow counters. A counter is taken at random from the bag.

The table shows the probabilities of getting a red counter or a yellow counter.

the number of blue counters: the number of green counters = 3: 4

Complete the table.

Work out the probability of getting 4 tails when the coin is thrown 4 times.

There are only blue cubes, red cubes and yellow cubes in a box. The table shows the probability of taking at random a blue cube from the box.

The number of red cubes in the box is the same as the number of yellow cubes in the box.

Complete the table.

There are 12 blue cubes in the box.

Work out the total number of cubes in the box.

There are only blue cubes, red cubes and yellow cubes in a box. The table shows the probability of taking at random a blue cube from the box.

The number of red cubes in the box is the same as the number of yellow cubes in the box.

Complete the table.

There are 12 blue cubes in the box.

Work out the total number of cubes in the box.

Mary travels to work by train every day. The probability that her train will be late on any day is 0.15

Complete the probability tree diagram for Thursday and Friday.

Work out the probability that her train will be late on at least one of these two days.

There are only red counters and blue counters in a bag.

Joe takes at random a counter from the bag. The probability that the counter is red is 0.65 Joe puts the counter back into the bag.

Mary takes at random a counter from the bag. She puts the counter back into the bag.

What is the probability that Joe and Mary take counters of different colours?

There are 78 red counters in the bag.

How many blue counters are there in the bag?

Here is a 4-sided spinner.

The table shows the probabilities that when the spinner is spun it will land on 1, on 3 and on 4

The spinner is spun once.

Work out the probability that the spinner will land on 2

Which number is the spinner least likely to land on?

Jake is going to spin the spinner 60 times.

Work out an estimate for the number of times the spinner will land on 1

A scout group has a raffle to raise money for charity. There is 1 prize to be won in the raffle.

Laura buys 12 raffle tickets. A total of 350 raffle tickets are sold.

Find the probability that Laura does not win the prize.

A darts team is going to play a match on Saturday and on Sunday. The probability that the team will win on Saturday is 0.45

If they win on Saturday, the probability that they will win on Sunday is 0.67 If they do not win on Saturday, the probability that they will win on Sunday is 0.35

Complete the probability tree diagram.

Find the probability that the team will win exactly one of the two matches.

There are some counters in a bag. The counters are red or white or blue or yellow.

Bob is going to take at random a counter from the bag.

The table shows each of the probabilities that the counter will be blue or will be yellow.

There are 18 blue counters in the bag.

The probability that the counter Bob takes will be red is twice the probability that the counter will be white.

Work out the number of red counters in the bag.

A marble is going to be taken at random from a box of marbles. The probability that the marble will be silver is 0.5

There must be an even number of marbles in the box.

Explain why.

When a biased 6-sided dice is thrown once, the probability that it will land on 4 is 0.65 The biased dice is thrown twice.

Amir draws this probability tree diagram. The diagram is not correct.

Write down two things that are wrong with the probability tree diagram.

There are some counters in a bag. The counters are red or white or blue or yellow.

Bob is going to take at random a counter from the bag.

The table shows each of the probabilities that the counter will be blue or will be yellow.

There are 18 blue counters in the bag.

The probability that the counter Bob takes will be red is twice the probability that the counter will be white.

Work out the number of red counters in the bag.

A marble is going to be taken at random from a box of marbles. The probability that the marble will be silver is 0.5

There must be an even number of marbles in the box.

Explain why.

The table shows the probabilities that a biased dice will land on 2, on 3, on 4, on 5 and on 6

Neymar rolls the biased dice 200 times.

Work out an estimate for the total number of times the dice will land on 1 or on 3

The table shows some information about the dress sizes of 25 women.

Find the median dress size.

3 of the 25 women have a shoe size of 7

Zoe says that if you choose at random one of the 25 women, the probability that she has either a shoe size of 7 or a dress size of 14 is because

Is Zoe correct? You must give a reason for your answer.