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Combined Probabilities (2)

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

'Combined Probabilities (2)' worksheet

Key stage:  KS 4

Curriculum topic:  Probability

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

Difficulty level:  

down

Worksheet Overview

QUESTION 1 of 10

If two events, A and B, do not affect each other then they are independent.

The probability of A and B happening is the product of their individual probabilities.

P (A and B) = P (A) x P (B)

 

Example

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

One counter is selected at random and replaced.

A second counter is then selected.

What is the probability that the first counter is red and the second counter is yellow?

 

Answer

P(red) = 4/15

P(yellow) = 6/15

P(red and yellow) = 4/15 x 6/15 = 24/225 = 8/75

A box of chocolates contains 5 dark chocolates, 2 white chocolates and 3 toffees.

 

One item is selected at random and then replaced.  A second item is then selected.

 

What is the probability that a dark chocolate is chosen followed by 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 5 £1 coins.

 

One coin is selected at random and replaced.  A second coin is then selected.

 

What is the probability that a 1p is chosen followed by a £1 coin?

 

(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 and then replaced before another counter is chosen.

 

What is the probability that a red counter is chosen followed by a blue one?

 

(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 and then replaced before a second counter is chosen.

 

What is the probability that we get a yellow counter followed by a blue one?

 

(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 and then replaced before another is chosen.

 

What is the probability that we get a red counter followed by a blue counter?

 

(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 and then replaced before choosing another.

 

What is the probability that a red ball is chosen followed by a yellow one?

 

(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 and replaced before another is chosen.

 

What is the probability that we get a red ball followed by a blue ball?

 

(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 9 toffees.

 

One item is selected at random and replaced before another is chosen.

 

What is the probability that we choose a white chocolate first and then a dark chocolate?

 

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

A bag of coins contains 14 1p coins, 10 10p coins and 4 £1 coins.

 

One coin is selected at random and then replaced before another is chosen.

 

What is the probability that two £1 coins are chosen?

 

(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 and replaced before another is chosen.

 

What is the probability that two 10p coins are chosen?

 

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

  • Question 1

A box of chocolates contains 5 dark chocolates, 2 white chocolates and 3 toffees.

 

One item is selected at random and then replaced.  A second item is then selected.

 

What is the probability that a dark chocolate is chosen followed by a toffee?

 

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

CORRECT ANSWER
3/20
EDDIE SAYS
5/10 × 3/10
  • Question 2

A bag of coins contains 15 1p coins, 10 10p coins and 5 £1 coins.

 

One coin is selected at random and replaced.  A second coin is then selected.

 

What is the probability that a 1p is chosen followed by a £1 coin?

 

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

CORRECT ANSWER
1/12
EDDIE SAYS
1/2 × 1/6
  • Question 3

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

 

One counter is selected at random and then replaced before another counter is chosen.

 

What is the probability that a red counter is chosen followed by a blue one?

 

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

CORRECT ANSWER
4/45
EDDIE SAYS
4/15 × 1/3
  • Question 4

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

 

One counter is selected at random and then replaced before a second counter is chosen.

 

What is the probability that we get a yellow counter followed by a blue one?

 

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

CORRECT ANSWER
2/15
EDDIE SAYS
6/15 × 1/3
  • Question 5

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

 

One counter is selected at random and then replaced before another is chosen.

 

What is the probability that we get a red counter followed by a blue counter?

 

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

CORRECT ANSWER
1/9
EDDIE SAYS
1/3 × 1/3
  • Question 6

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

 

One ball is selected at random and then replaced before choosing another.

 

What is the probability that a red ball is chosen followed by a yellow one?

 

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

CORRECT ANSWER
25/144
EDDIE SAYS
5/12 × 5/12
  • Question 7

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

 

One ball is selected at random and replaced before another is chosen.

 

What is the probability that we get a red ball followed by a blue ball?

 

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

CORRECT ANSWER
5/44
EDDIE SAYS
5/22 × 1/2
  • Question 8

A box of chocolates contains 15 dark chocolates, 16 white chocolates and 9 toffees.

 

One item is selected at random and replaced before another is chosen.

 

What is the probability that we choose a white chocolate first and then a dark chocolate?

 

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

CORRECT ANSWER
3/20
EDDIE SAYS
16/40 × 15/40
  • Question 9

A bag of coins contains 14 1p coins, 10 10p coins and 4 £1 coins.

 

One coin is selected at random and then replaced before another is chosen.

 

What is the probability that two £1 coins are chosen?

 

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

CORRECT ANSWER
1/49
EDDIE SAYS
1/7 × 1/7
  • Question 10

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

 

One coin is selected at random and replaced before another is chosen.

 

What is the probability that two 10p coins are chosen?

 

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

CORRECT ANSWER
9/25
EDDIE SAYS
3/5 × 3/5
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