Conditional probability

Here is a biased 5-sided spinner. When the spinner is spun, it can land on blue or on green or on purple or on red or on yellow.

The table gives information about the probability of the spinner landing on each colour.

Sophie spins the spinner once.

Work out the probability that the spinner lands on blue or on green or on purple.

Max spins the spinner 350 times.

Work out an estimate for the number of times the spinner lands on red.

Kannika has 9 counters. There is a number on each counter.

Kannika puts the 9 counters in a bag. She takes at random a counter from the bag and does not replace the counter. She then takes at random a second counter from the bag.

Work out the probability that the sum of the numbers on the two counters is less than 5

There are 25 counters in a bag such that

6 counters are blue x counters are orange, where x > 9 the rest of the counters are pink

Maalam takes at random two of the counters from the bag. The probability that Maalam takes one orange counter and one pink counter is Calculate the probability that Maalam takes 2 pink counters from the bag. Show clear algebraic working.

In a bag, there are only red counters, blue counters, green counters and yellow counters.

The total number of counters in the bag is 80

In the bag

the number of red counters is x + 7 the number of blue counters is x – 11 the number of green counters is 3x

Jude takes at random a counter from the bag. The probability that he takes a red counter is

Work out the probability that Jude takes a yellow counter.

The table gives information about the time taken by each student in Year 11 to complete a homework task.

Time taken (t minutes)	Frequency
10 t 25	15
25 t 30	18
30 t 50	32
50 t 60	4

On the grid, draw a histogram for this information.

One of these students who took 50 minutes or less and more than 25 minutes to complete this homework task is chosen at random.

Find an estimate for the probability that this student took 45 minutes or less to complete this homework task.

Elliot has x counters.

Each counter has one red face and one green face.

Elliot spreads all the counters out on a table and sees that the number of counters showing a red face is 5

Elliot then picks at random one of the counters and turns the counter over. He then picks at random a second counter and turns the counter over. The probability that there are still 5 counters showing a red face is

Work out the value of x Show clear algebraic working.

The table gives information about the times, in minutes, taken by 80 customers to do their shopping in a supermarket.

Time taken (t minutes)	Frequency
0 t 10	7
10 t 20	26
20 t 30	24
30 t 40	14
40 t 50	7
50 t 60	2

Complete the cumulative frequency table.

On the grid opposite, draw a cumulative frequency graph for your table.

Time taken (minutes)

Use your graph to find an estimate for the median time taken.

One of the 80 customers is chosen at random.

Use your graph to find an estimate for the probability that the time taken by this customer was more than 42 minutes.

The histogram gives information about the heights, h cm, of some tomato plants.

There are 12 tomato plants for which 75 < h 85 One of the tomato plants is selected at random.

Find an estimate for the probability that this tomato plant has a height greater than 82.5 cm

In a bag, there are only

3 blue beads 4 white beads and x orange beads.

Jean is going to take at random two beads from the bag. The probability that Jean will take two beads of the same colour is Find the total number of beads in the bag. Show clear algebraic working.

The table shows information about the weights, in kilograms, of 40 babies.

Weight (wkg)	Frequency
2 w 3	12
3 w 4	16
4 w 5	9
5 w 6	2
6 w 7	1

Write down the modal class.

Work out an estimate for the mean weight of the 40 babies.

One of the 40 babies is going to be chosen at random.

Find the probability that this baby has a weight of more than 5 kg.

There are 16 sweets in a bowl.

4 of the sweets are blackcurrant. 5 of the sweets are lemon. 7 of the sweets are orange.

Anna, Ravi and Sam each take at random one sweet from the bowl.

Work out the probability that the 5 lemon sweets are still in the bowl.

In group C, there are 6 girls and 8 boys. In group D, there are 3 girls and 7 boys.

A team is made by picking at random one child from group C and one child from group D.

Complete the probability tree diagram.

Work out the probability that there are two boys in the team.

After the first team has been picked, a second team is picked. One child is picked at random from the children left in group C and one child is picked at random from the children left in group D.

Work out the probability that there are two boys in each of the two teams.

Each day that Barney goes to college, he either goes by bus or he walks. The probability that Barney will go to college by bus on any day is 0.3

When Barney goes to college by bus, the probability that he will be late is 0.2 When Barney walks to college, the probability that he will be late is 0.1

Complete the probability tree diagram.

Barney will go to college on 200 days next year.

Work out an estimate for the number of days Barney will be late for college next year.

The histogram shows information about the ages of all the passengers travelling on a plane. No one on the plane is older than 80 years.

24 passengers on the plane are aged between 40 years and 60 years.

Work out the total number of passengers on the plane.

A passenger on the plane is picked at random.

Work out an estimate for the probability that this person is older than 55 years.

A box contains marbles.

4 of the marbles are red. The rest of the marbles are yellow.

Antonia takes at random a marble from the box and does not replace it. Sergio then takes at random a marble from the box.

The probability that Antonia and Sergio both take a yellow marble is 0.7

Work out how many marbles were originally in the box. Show your working clearly.

There are 8 counters in a bag. There is a number on each counter.

Fiona takes at random three of the counters. She adds the numbers on the three counters to get her total.

Work out the probability that her total is an odd number.