The probability that he misses his first two shots and makes the third is about 1.3%
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Further explanation
The probability of an event is defined as the possibility of an event occurring against sample space.
[tex]\large { \boxed {P(A) = \frac{\text{Number of Favorable Outcomes to A}}{\text {Total Number of Outcomes}} } }[/tex]
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Permutation ( Arrangement )
Permutation is the number of ways to arrange objects.
[tex]\large {\boxed {^nP_r = \frac{n!}{(n - r)!} } }[/tex]
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Combination ( Selection )
Combination is the number of ways to select objects.
[tex]\large {\boxed {^nC_r = \frac{n!}{r! (n - r)!} } }[/tex]
Let us tackle the problem.
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A professional basketball player makes (scores) free throw shots 88% of the time.
Let:
Probability of making (scoring) free throw shots = P(A) = 88%
Probability of missing free throw shots = P(A') = (100 - 88)% = 12%
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The probability that he misses his first two shots and makes the third:
[tex]P(A' \cap A' \cap A) = P(A') \times P(A') \times P(A)[/tex]
[tex]P(A' \cap A' \cap A) = ( P(A') )^2 \times P(A)[/tex]
[tex]P(A' \cap A' \cap A) = ( 12 \% )^2 \times 88 \%[/tex]
[tex]P(A' \cap A' \cap A) = 1.2672 \%[/tex]
[tex]P(A' \cap A' \cap A) \approx 1.3 \%[/tex]
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Learn more
- Different Birthdays : https://brainly.com/question/7567074
- Dependent or Independent Events : https://brainly.com/question/12029535
- Mutually exclusive : https://brainly.com/question/3464581
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Answer details
Grade: High School
Subject: Mathematics
Chapter: Probability
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Keywords: Probability , Sample , Space , Six , Dice , Die , Binomial , Distribution , Mean , Variance , Standard Deviation
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