Edexcel IGCSE Math A 6.3.HB Probabilities of Independent Events

Practise multiplying independent-event probabilities and adding mutually exclusive paths for combined outcomes.

Exam points

multiply probabilities along one independent path to find a combined outcome
add mutually exclusive path probabilities for same, different or majority outcomes
use a given joint probability and independence to recover an unknown event probability

[Maximum number: 3]

Emilie takes part in two races.
The probability that she wins the first race is 0.7
The probability that she wins the second race is 0.4
The outcomes of the two races are independent.

Work out the probability that Emilie wins exactly one of the two races.

Emilie is going to take part in a third race.
If she wins both of the first two races, the probability that she will win the third race is 0.6 If she wins exactly one of the first two races, the probability that she will win the third race is 0.3

Exactly one win:
$0.7\times0.6+0.3\times0.4 = 0.42+0.12 = 0.54$
Final answer:
0.54
Equivalent answer $\frac{27}{50}$ accepted.

All question bank results loaded

6.3.HB The probability that two or more independent events question 1