The probability that a certain person will buy a shirt is 0.2, the probability that he will buy a coat is 0.3 and the probability that he will buy a shirt given that he buys a coat is 0.4. Find the probability that he will buy both a shirt and a coat.
Let P(A) be the probability of a certain person buying a shirt.
∴P(A)=0.2
Let P(B) be the probability of him buying a coat.
∴P(B)=0.3
Let 
be the probability that he buys both a shirt and a coat.
Tip – By conditional probability, 
where 
is the probability of occurrence of the event A given that B has already occurred.
The probability that he will buy a shirt given that he buys a coat:
⇨P(A∩B)=P(B)P(A⁄B)
=0.3×0.4
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