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Alex787 [66]
3 years ago
10

A softball pitcher has a 0.675 probability of throwing a strike for each pitch and a 0.325 probability of throwing a ball. If th

e softball pitcher throws 29 pitches, we want to know the probability that exactly 19 of them are strikes.
Mathematics
1 answer:
Dafna11 [192]3 years ago
8 0

Answer:

The probability that exactly 19 of them are strikes is 0.1504

Step-by-step explanation:

The binomial probability parameters given are;

The probability that the pitcher throwing a strike, p = 0.675

The probability that the pitcher throwing a ball. q = 0.325

The binomial probability is given as follows;

p(x) = _{n}C_{x}\cdot p^{x}\cdot q^{1-x}

Where:

x = Required probability

Therefore, the probability that the pitcher throws 19 strikes out of 29 pitches is found as follows;

The probability that exactly 19 of them are strikes is given as follows;

\binom{29}{19}(0.675)^{19}0.325^{10} = \frac{29!}{19!\times 10!}\times (0.675)^{19}\times 0.325^{10} = 0.1504

Hence the probability that exactly 19 of them are strikes = 0.1504

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