The probability that exactly 19 of them are strikes is 0.1504.
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;
[tex]p(x) = _nC_x . p^x . q^{1-x}[/tex]
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;
[tex]\frac{29}{19}(0.675)^{19}0.325^{10} = \frac{29!}{19! * 10!} * (0.675)^{19} * 0.325^{10}[/tex]
= 0.1504
Hence the answer is the probability that exactly 19 of them are strikes = 0.1504.
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