rafaellareale wrote:
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
There are 2 penalty kicks that the soccer player will take.
The probability of scoring a goal is 80% or \(\frac{4}{5}\). The probability of not scoring a goal is \(1 - \frac{4}{5} = \frac{1}{5}\)
There are 3 possibilities where he is going to miss at least one goal
1. When the soccer player misses the first goal and scores the second goal = \(\frac{1}{5}*\frac{4}{5} = \frac{4}{25}\)
2. When the soccer player scores the first goal and misses the second goal = \(\frac{4}{5}*\frac{1}{5} = \frac{4}{25}\)
3. When the soccer player misses both goals = \(\frac{1}{5}*\frac{1}{5} = \frac{1}{25}\)
Therefore, the total probability that the soccer player misses at least one goal is \(\frac{4}{25} + \frac{4}{25} + \frac{1}{25} = \frac{9}{25}\)
(Option D)
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