CAIE S1 2023 March — Question 4

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2023
SessionMarch
TopicConditional Probability
TypeProbability with replacement vs without replacement

4 The probability that it will rain on any given day is \(x\). If it is raining, the probability that Aran wears a hat is 0.8 and if it is not raining, the probability that he wears a hat is 0.3 . Whether it is raining or not, if Aran wears a hat, the probability that he wears a scarf is 0.4 . If he does not wear a hat, the probability that he wears a scarf is 0.1 . The probability that on a randomly chosen day it is not raining and Aran is not wearing a hat or a scarf is 0.36 . Find the value of \(x\).