Question

A martial artist is practicing breaking 5 boards. He is able to break a board with probability 0.8. (a) What is the probability that he breaks exactly 2 out of the 5 boards that are placed before him? (b) What is the probability that he breaks at most 3 out of the 5 boards that are placed before him? (c) What is the expected number of boards he will break?

Answer 1

(a) = 0.32 or 8/25

(b) = 0.48 or 12/25

(c) = 4 Boards

Explanation:

(a):

0.8 x 2/5

8/10 x 4/10

(8 x 4) / (10 x 10)

(32) / (100)

0.32 or 8/25

(b):

0.8 x 3/5

8/10 x 6/10

(8 x 6) / (10 x 10)

(48) / (100)

0.48 or 12/25

(c):

0.8 x 5

8/10 x 50/10

(8 x 50) / (10 x 10)

(400) / (100)

4 Boards