Question

A coin is tossed 12 times. What is the probability of obtaining five heads and seven tails?

Answer 1

99/512 = 0.193359375

Explanation:

Each sequence of 5 H's and 7 T's has probability of occurring equal to 1/2^12 (1 divided by 2 to the twelfth power).

Since the number of 5 H, 7 T sequences is equal to C(12,5) = the number of combinations of 12 things taken 5 at a time =

12 * 11 * 10 * 9 * 5 / (5 * 4 * 3 * 2 * 1) =

792,

we have that the probability of obtaining 5 H's and 7 T's =

the sum of the probabilities of all of the sequences =

1/2^12 + 1/2^12 + 1/2^12 + . . . + 1/2^12, 792 times =

792(1/2^12) =

99 / 2^9 =

99 /512 =

0.193359375

Answer 2

I believe the probability would be 0.19336