# Combined Probabilities (1)

In this worksheet, students understand the concept of mutually exclusive events and work out combined probabilities.

Key stage:  KS 4

Curriculum topic:  Probability

Curriculum subtopic:  Calculate the Probability of Independent and Dependent Combined Events

Difficulty level:

### QUESTION 1 of 10

If two events, A and B, cannot happen at the same time, they are called mutually exclusive.

The probability of A or B happening is the sum of their individual probabilities.

P (A or B) = P (A) + P (B)

Example

A bag contains 4 red counters, 5 blue counters and 6 yellow counters.

One counter is selected at random.

What is the probability that it is red or yellow?

P(red) = 4/15

P(yellow) = 6/15

P(red or yellow) = 4/15 + 6/15 = 10/15 = 2/3

A bag contains 4 red counters, 5 blue counters and 6 yellow counters.

One counter is selected at random.

What is the probability that it is yellow or blue?

(Write your answer as a fraction in its lowest terms in the form a/b)

A bag contains 4 red counters, 5 blue counters and 6 yellow counters.

One counter is selected at random.

What is the probability that it is red or blue?

(Write your answer as a fraction in its lowest terms in the form a/b)

A bag contains 5 red counters, 5 blue counters and 5 yellow counters.

One counter is selected at random.

What is the probability that it is red or blue?

(Write your answer as a fraction in its lowest terms in the form a/b)

A bag contains 5 red balls, 2 blue balls and 5 yellow balls.

One ball is selected at random.

What is the probability that it is red or yellow?

(Write your answer as a fraction in its lowest terms in the form a/b)

A bag contains 5 red balls, 11 blue balls and 6 yellow balls.

One ball is selected at random.

What is the probability that it is red or yellow?

(Write your answer as a fraction in its lowest terms in the form a/b)

A box of chocolates contains 5 dark chocolates, 6 white chocolates and 3 toffees.

One item is selected at random.

What is the probability that it is a dark chocolate or a toffee?

(Write your answer as a fraction in its lowest terms in the form a/b)

A box of chocolates contains 15 dark chocolates, 16 white chocolates and 11 toffees.

One item is selected at random.

What is the probability that it is a white chocolate or a toffee?

(Write your answer as a fraction in its lowest terms in the form a/b)

A bag of coins contains 15 1p coins, 10 10p coins and 3 £1 coins.

One coin is selected at random.

What is the probability that it is a 1p or a £1 coin?

(Write your answer as a fraction in its lowest terms in the form a/b)

A bag of coins contains 15 1p coins, 10 10p coins and 3 £1 coins.

One coin is selected at random.

What is the probability that it is not a £1 coin?

(Write your answer as a fraction in its lowest terms in the form a/b)

A bag of coins contains 4 1p coins, 12 10p coins and 4 £1 coins.

One coin is selected at random.

What is the probability that it is a 1p or a 10p coin?

(Write your answer as a fraction in its lowest terms in the form a/b)

• Question 1

A bag contains 4 red counters, 5 blue counters and 6 yellow counters.

One counter is selected at random.

What is the probability that it is yellow or blue?

(Write your answer as a fraction in its lowest terms in the form a/b)

11/15
• Question 2

A bag contains 4 red counters, 5 blue counters and 6 yellow counters.

One counter is selected at random.

What is the probability that it is red or blue?

(Write your answer as a fraction in its lowest terms in the form a/b)

3/5
EDDIE SAYS
9/15
• Question 3

A bag contains 5 red counters, 5 blue counters and 5 yellow counters.

One counter is selected at random.

What is the probability that it is red or blue?

(Write your answer as a fraction in its lowest terms in the form a/b)

2/3
EDDIE SAYS
10/15
• Question 4

A bag contains 5 red balls, 2 blue balls and 5 yellow balls.

One ball is selected at random.

What is the probability that it is red or yellow?

(Write your answer as a fraction in its lowest terms in the form a/b)

5/6
EDDIE SAYS
10/12
• Question 5

A bag contains 5 red balls, 11 blue balls and 6 yellow balls.

One ball is selected at random.

What is the probability that it is red or yellow?

(Write your answer as a fraction in its lowest terms in the form a/b)

1/2
EDDIE SAYS
11/22
• Question 6

A box of chocolates contains 5 dark chocolates, 6 white chocolates and 3 toffees.

One item is selected at random.

What is the probability that it is a dark chocolate or a toffee?

(Write your answer as a fraction in its lowest terms in the form a/b)

4/7
EDDIE SAYS
8/14
• Question 7

A box of chocolates contains 15 dark chocolates, 16 white chocolates and 11 toffees.

One item is selected at random.

What is the probability that it is a white chocolate or a toffee?

(Write your answer as a fraction in its lowest terms in the form a/b)

9/14
EDDIE SAYS
27/42
• Question 8

A bag of coins contains 15 1p coins, 10 10p coins and 3 £1 coins.

One coin is selected at random.

What is the probability that it is a 1p or a £1 coin?

(Write your answer as a fraction in its lowest terms in the form a/b)

9/14
EDDIE SAYS
18/28
• Question 9

A bag of coins contains 15 1p coins, 10 10p coins and 3 £1 coins.

One coin is selected at random.

What is the probability that it is not a £1 coin?

(Write your answer as a fraction in its lowest terms in the form a/b)

25/28
• Question 10

A bag of coins contains 4 1p coins, 12 10p coins and 4 £1 coins.

One coin is selected at random.

What is the probability that it is a 1p or a 10p coin?

(Write your answer as a fraction in its lowest terms in the form a/b)

4/5
EDDIE SAYS
16/20
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