In an experiment, a fair coin is tossed 9 times and the face that appears (H for

Question

In an experiment, a fair coin is tossed 9 times and the face that appears (H for head or T for tail) for each toss is recorded. How many elements of the sample space will have no tails? _____ How many elements of the sample space will have exactly one tail? ______ How many elements of the sample space will start and end with different faces and have a total of exactly two tails? _____ How many elements of the sample space will start and end with a tail and include a total of exactly three tails? _____

Explanation / Answer

1. No tails will occur when all the 9 outcomes are heads. No of elements = 9C9 = 1

2. Similarly, exactly one tail occurs 9C8 = 9 times

3. Possible outcomes are TXXXXXXXH or HXXXXXXXT, where only one of XXXXXX is T, as we want exactly 2 tails and we already have a tail at the beginning or the end. So, possible outcomes are 7C1 + 7C1 = 14

4. Possible outcomes are TXXXXXXXT, where only one of XXXXXX is T, as we want exactly 3 tails and we already have 2 tails. So, possible outcomes are 7C1 = 7

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