Question

assume that a softball player has 0.72 probability of getting a hit in each at bat. assume that the player bats four times. what is the probability that she gets a hit only in her first at bat? the probability is (round to four decimal places as needed.)

Explanation:

Step1: Calculate the probability of getting a hit in the first at - bat

The probability of getting a hit in one at - bat is \(p = 0.72\).

Step2: Calculate the probability of not getting a hit in the remaining three at - bats

The probability of not getting a hit in one at - bat is \(q=1 - p=1 - 0.72 = 0.28\).
Since the at - bats are independent events, the probability of not getting a hit in three at - bats is \(q\times q\times q=0.28^{3}\).

Step3: Calculate the overall probability

The probability that she gets a hit only in her first at - bat is \(P = 0.72\times0.28^{3}\).

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Answer:

\(0.0158\)