Consider the experiment of throwing a die, if a multiple of 3 comes up 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 2. We will break down the solution 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 a multiple of 3 (which are 3 and 6) comes up, we throw the die again. If any other number (1, 2, 4, 5) comes up, we toss a coin.

### Step 2: Identify Events
- Let event E be the event that the coin shows a tail.
- Let event F be the event that at least one die shows a 2.
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