A fair coin is tossed until a head or five tails occur. If X denotes the number of tosses of the coin, find mean of X.

Explanation

To find the mean of the random variable \( X \), which denotes the number of tosses of a fair coin until a head or five tails occur, we can follow these steps:

### Step 1: Define the Sample Space
The outcomes of tossing a fair coin until we get a head or five tails can be outlined as follows:
- \( H \) (Head) on the first toss: \( X = 1 \)
- \( TH \) (Tail, Head): \( X = 2 \)
- \( TTH \) (Tail, Tail, Head): \( X = 3 \)
- \( TTTH \) (Tail, Tail, Tail, Head): \( X = 4 \)
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