Question

Write 15 probability measures for flipping a coin 3 times:

Answer 1

The sample space for flipping a coin 3 times:

S = { HHH, HHT, HTH, HTT, THH, THT, TTH, TTT }

here we assume a fair coin.

The probability measures that is probabilities of the occurring different events using above assumption are as follow.

1. P( exactly 3 heads ) = 1/8

2. P( exactly 3 Tails) = 1/8

3. P( exactly 2 heads ) = 3/8

4. P(exactly 2 tails) = 3/8

5. P(exactly 1 heads) = 3/8

6. P(exactly 1 tails) = 3/8

7. P( four heads) = 0

8. P( at least 1 heads) = 7/8

9. P( at least 1 tails) = 7/8

10. P(at least 2 heads) = 4/8 = 1/2

11. P(at least 2 tails) = 4/8 = 1/2

12. P(at most 3 heads ) = 8/8 = 1

13. P( less than 2 heads ) = 4/8 = 1/2

14. P(less than 2 tails ) = 4/8 = 1/2

15. P( less than 3 heads) = 7/8

16. P( alternative H and T ) = P( HTH, THT) = 2/8 = 1/4