Question

Messi is one of the best soccer players in the world. Messi makes 78% of the penalty kicks that he takes. Suppose that next season he will take 8 penalty kicks. What is the probability that he will make either 7 or 8 of those kicks?

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Darrell

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77 Answers

1. Identify the given values:

n = 8

p = 0.78

k_1 = 7

k_2 = 8

2. Calculate the binomial coefficient for \( k = 7 \):

\binom{8}{7} = 8

3. Calculate the probability for \( k = 7 \):

P(X=7)=8\cdot(0.78)^7\cdot(0.22)^1\approx0.30915

4. Calculate the binomial coefficient for \( k = 8 \):

\binom{8}{8} = 1

5. Calculate the probability for \( k = 8 \):

P(X=8)=1\cdot(0.78)^8\cdot(0.22)^0\approx0.13701

6. Add the probabilities together:

P(X=7\text{ or }X=8)\approx0.30915+0.13701=0.44616

Therefore, the probability that Messi will make either 7 or 8 penalty kicks out of 8 is approximately0.44616 .

2. Calculate the binomial coefficient for \( k = 7 \):

3. Calculate the probability for \( k = 7 \):

4. Calculate the binomial coefficient for \( k = 8 \):

5. Calculate the probability for \( k = 8 \):

6. Add the probabilities together:

Therefore, the probability that Messi will make either 7 or 8 penalty kicks out of 8 is approximately

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