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Sagot :
The probability that exactly 12 of them are strikes is 0.09.
In this question,
Number of pitches, n = 22
Probability of throwing a strike for each pitch, p = 0.431
Then, q = 1 - p
⇒ q = 1 - 0.431
⇒ q = 0.569
Number of strikes, x = 12
The probability that exactly 12 of them are strikes can be calculated using Binomial expansion,
[tex]P(X=x)=nC_xP^{x}q^{(n-x)}[/tex]
⇒ [tex]P(X=12)=22C_{12}(0.431)^{12}(0.569)^{(22-12)}[/tex]
⇒ [tex]P(X=12)=22C_{12}(0.431)^{12}(0.569)^{10}[/tex]
⇒ [tex]P(X=12)=(\frac{22!}{12!10!} )(0.431)^{12}(0.569)^{10}[/tex]
⇒ P(X=12) = (646646)(0.000041)(0.00355)
⇒ P(X=12) = 0.09431 ≈ 0.09
Hence we can conclude that the probability that exactly 12 of them are strikes is 0.09.
Learn more about probability here
https://brainly.com/question/24180142
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