Analysis and Approaches for IBDP Maths Ebook 2 | Page 237

74
Paper 2 Section A – Bayes’ Theorem Involving 2 Events
Example
A virus is spreading in a town, and a vaccination is available to protect against the virus.
68% of the population has been vaccinated. If a person has had the vaccination, the
probability of catching the virus is 0.08; without the vaccination, the probability is 0.34.
(a)
(b)
Find the exact probability that a randomly selected person catches the virus.
A randomly chosen person catches the virus. Find the probability that this
person has not been vaccinated.
[3]
[3]
Solution
17
(a)
(b)
The required probability
� (68%)(0.08) � (1 � 68%)(0.34)
M1A1
� 0.1632
A1
The required probability
(1 � 68%)(0.34)
�
0.1632
M1A1
2
�
3
A1
[3]
[3]
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