Analysis of questionnaire completed by holiday makers showed that 0.75 classified their holiday as excellent at Malindi. The probability of hot weather in the resort is 0.6. If the probability of regarding holiday as excellent given hot weather is 0.9, what is the probability that there was hot weather if a holiday maker considers his holiday excellent?
SOLUTION
P(A|B) = ( P(A) * P(B|A))/P(B)
Assume H = hot weather
G = Good
P(G) = 0.75
P(H) = 0.6 and
P(G|H) = 0.9 (Probability of regard holiday as good described hot weather)
Now the question needs us to get
P(H|G) = Probability of (there was) hot weather given that the holiday has been rated as good).
P(H|G) = ( P(H) * P(G|H))/P(G)
=(0.6)(0.9)/0.75
= 0.72.