A soccer player has 80% chance of scoring a goal at his penalty kicks.

Question:
A soccer player has 80% chance of scoring a goal at his penalty kicks. What is the probability that he is going to miss at least a goal in two penalty kicks?
(A) 0
(B) 16/25
(C) 12/25
(D) 9/25
(E) 1/25


Solution:
Probability that the player will score = 0.8
=> Probability that the player will miss = 1 - 0.8 = 0.2

Out of 2 shots, he can miss at least one if:
#a) He misses the first and scores the second = 0.2 x 0.8 = 0.16
Or
#b) He scores the first and misses the second = 0.2 x 0.8 = 0.16
Or
#c) He misses the first and misses the second = 0.2 x 0.2 = 0.04

Thus, the required probability = 0.16 + 0.16 + 0.04 = 0.36


Alternate approach:
Probability that, out of 2 shots, he misses at least one
= 1 - Probability that, out of 2 shots, he misses none
= 1 - Probability that he scores the first and scores the second
= 1 - 0.8 x 0.8
= 1 - 0.64
= 0.36
= 36/100 = 9/25

Answer D