Analysis and Approaches for IBDP Maths Ebook 2 | Page 239

75
Paper 2 Section A – Bayes’ Theorem Involving 3 Events
Example
Stacy has three ways of getting to work. 25% of the time she travels by bus, 35% of the
time she rides her bicycle and 40% of the time she walks. When travelling by bus, Stacy
is late 10% of the time. When riding her bicycle she is late 20% of the time. When
walking she is late 35% of the time.
(a)
(b)
Find the probability that she is late.
Given that she was late, find the probability that she travels by bus.
[3]
[3]
Solution
17
(a)
(b)
The required probability
� (25%)(10%) � (35%)(20%) � (40%)(35%) M1A1
� 0.235
A1
The required probability
(25%)(10%)
�
0.235
M1A1
5
�
47
A1
[3]
[3]
Exercise 75
1. In a school, there are 145 students studying only one subject from Japanese, Korean and
Portuguese. There are 35 students studying Japanese, of whom 20 are male. There are 60
students studying Korean, of whom 18 are male. For students studying Portuguese, the
ratio of the number of male students to that of female students is 3:2.
(a)
(b)
One student is randomly chosen. Find the probability that he is a male.
Given that a male student is chosen, find the probability that he studies
Portuguese.
[3]
[3]
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