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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Answer to a math 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?
Darrell
4.5100 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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