Consider the experiment of throwing a die. if a multiple of 3 comes tip. throw the die again and if any other number comes, toss a coin Find the conditional probability of the event the coin shows a tail, given that at least one die shows a 3.

Explanation

To solve the problem, we need to find the conditional probability of the event that the coin shows a tail, given that at least one die shows a 3. Let's break this down step by step.

### Step 1: Define the Sample Space
When we throw a die, the possible outcomes are {1, 2, 3, 4, 5, 6}. If we roll a multiple of 3 (which are 3 and 6), we throw the die again. If we roll any other number (1, 2, 4, 5), we toss a coin.

- If we roll a 3, the outcomes of the second die are {1, 2, 3, 4, 5, 6}.
- If we roll a 6, the outcomes of the second die are also {1, 2, 3, 4, 5, 6}.
- If we roll 1, 2, 4, or 5, we toss a coin which can show either Head (H) or Tail (T).
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