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Probabilities are used to determine the chances of an event.
The probability that he hits exactly 2 in the next 7 bats is 0.3039
The given parameters are:
[tex]\mathbf{p = 0.235}[/tex] --- probability that he hits a bat
The question is an illustration of binomial probability, and it is represented as:
[tex]\mathbf{Pr = ^nC_xp^x(1 - p)^{n -x}}[/tex]
In this case:
[tex]\mathbf{n = 7}[/tex] --- number of bats
[tex]\mathbf{x = 2}[/tex] --- number of hits
So, we have:
[tex]\mathbf{Pr = ^nC_xp^xq^{n -x}}[/tex]
[tex]\mathbf{Pr = ^7C_2 \times (0.235)^2 \times (1 - 0.235)^{7 -2}}[/tex]
[tex]\mathbf{Pr = 21 \times (0.235)^2 \times (0.765)^5}[/tex]
[tex]\mathbf{Pr = 0.3039}[/tex]
Hence, the probability that he hits exactly 2 in the next 7 bats is 0.3039
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