The probability that a certain person will buy a shirt is 0.2, the probability that he will buy a trouser is 0.3, and the probability that he will buy a shirt given that he buys a trouser is 0.4. Find the probability that he will buy both a shirt and a trouser. Find also the probability that he will but a trouser given that he buys a shirt.

Explanation

To solve the problem, we need to use the information given about the probabilities of buying a shirt and trouser, as well as the conditional probability.

Let's denote:
- \( P(S) \) = Probability of buying a shirt = 0.2
- \( P(T) \) = Probability of buying a trouser = 0.3
- \( P(S|T) \) = Probability of buying a shirt given that he buys a trouser = 0.4

### Step 1: Find the probability that he will buy both a shirt and a trouser.
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