Conditional Probability (CIE IGCSE Maths: Extended)

The diagram shows six discs.
Each disc has a colour and a number.

Two of the six discs are picked at random without replacement.

Find the probability that 

Morgan picks two of these letters, at random, without replacement.

Find the probability that he picks two letters that are the same.

{students in a school}
{students who play football}
{students who play baseball}
 
There are 240 students in the school.
 
• 120 students play football
• 40 students play baseball 
• 90 students play football but not baseball.

Complete the Venn diagram to show this information.
 

Two students who play baseball are chosen at random.
 
Find the probability that they both also play football.

Esme has a bag with 5 green counters and 4 red counters.
She takes three counters at random from the bag without replacement.
 
Work out the probability that the three counters are all the same colour.

Talika has a bag which contains 10 red balls and 8 blue balls.
Talika takes three balls at random from her bag, without replacement.
 
Calculate the probability that the three balls are the same colour.

Bag A contains 3 black balls and 2 white balls.
Bag B contains 1 black ball and 3 white balls.
A ball is taken at random from each bag.

[1]

[3]

The balls are returned to their original bags.
Three balls are taken at random from bag A, without replacement.

[2]

[1]

The balls are returned to their original bags.
A ball is taken at random from bag A and its colour is recorded.
This ball is then placed in bag B.
A ball is then taken at random from bag B.
 
Find the probability that the ball taken from bag B has a different colour to the ball taken from bag A.

The heights, metres, of the 120 boys in an athletics club are recorded.
The table shows information about the heights of the boys.

Height ( metres)
Frequency	7	18	30	24	27	14

Three boys are chosen at random from the club.

Calculate the probability that one of the boys has a height greater than 1.8 m and the other two boys each have a height of 1.4 m or less.

The 200 students also estimate the total area, , of the windows in the classroom.
The table shows their results.

Area (m2)
Frequency	32	64	80	24

Two students are chosen at random from those students that estimated the area of the windows to be more than .
 
Find the probability that one of the two students estimates the area to be greater than and the other student estimates the area to be  or less.

A box contains 20 packets of potato chips.
6 packets contain barbecue flavoured chips.
10 packets contain salt flavoured chips.
4 packets contain chicken flavoured chips.
Maria takes two packets at random without replacement.

Find the probability that she takes two packets of different flavoured chips.

 
The Venn diagram above shows information about the number of students who study Music (M), Drama (D) and Geography (G).

Two students are chosen at random from those who study Drama.
 
Calculate the probability that they both also study Music.

Sonia has a bag containing 20 sweets.
In the bag, there are 5 red, 6 green and 9 yellow sweets.
Sonia chooses two sweets at random, without replacement, from the bag.

i)

Show that the probability that she chooses two green sweets is .

[2]

[4]

Morgan picks three of these letters, at random, without replacement.

Find the probability that

This year, 40 students have each travelled by one or more of plane (), train () or boat ().

7 have travelled only by plane.
11 have travelled only by train.
9 have travelled only by boat.

Complete the Venn diagram.

Two students are chosen at random.

Calculate the probability that they both have travelled only by plane.

Two students are chosen at random from those who have travelled by train.

Calculate the probability that they both have also travelled by plane.

Angelo has a bag containing 3 white counters and black counters.
He takes two counters at random from the bag, without replacement.

Complete the following statement.
 
The probability that Angelo takes two black counters is

The probability that Angelo takes two black counters is .

The diagram shows two sets of cards.

Lena chooses three cards at random from Set C without replacement.

Find the probability that the third card chosen is numbered 4.

Suleika has six cards numbered 1 to 6.

Suleika takes two cards at random, without replacement.

[3]

[3]

The diagram shows 5 cards.

Donald chooses two of the five cards at random, without replacement.
He works out the total number of dots on these two cards.

[3]

[3]

A box contains 20 packets of potato chips.
6 packets contain barbecue flavoured chips.
10 packets contain salt flavoured chips.
4 packets contain chicken flavoured chips.
 
Maria takes three packets at random, without replacement, from the 20 packets.

Find the probability that she takes at least two packets of chicken flavoured chips.