This question is based on probability distribution. Therefore, the probability distribution for X are ,P(X=0) = 0.022 ,P(X=1) = 0.169, P(X=2) = 0.435 and P(X=3) = 0.373.
Given:
The probability that Roberto throws a baseball in the strike zone on one pitch is 0.72. Roberto throws a baseball 3 times in a row.
We need to determined the probability distribution for X ,the number of times Roberto throws the baseball in the strike zone.
According to the question,
By using the combination formula, we have to solve it,
It is given that n = 3 and p = 0.72.
Now calculating the P(X=0), we get,
\(P(X=0) = 3_{C_0}(0.72)^0(0.28)^3 \\P(X=0) = 0.022\)
Now calculating the P(X=1), we get,
\(P(X=1) = 3_{C_0}(0.72)^1(0.28)^2 \\P(X = 1)= 0.169\)
Now calculating the P(X=2), we get,
\(P(X=2) = 3_{C_0} (0.72)^2(0.28)^1 \\P(X=2) = 0.435\)
Now calculating the P(X=3), we get,
\(P(X=3) = 3_{C_0} (0.72)^3(0.28)^0\\P(X=3) = 0.373\)
Therefore, the probability distribution for X are ,P(X=0) = 0.022 ,P(X=1) = 0.169, P(X=2) = 0.435 and P(X=3) = 0.373.
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https://brainly.com/question/14210034
