Suppose the probability that a softball player gets a hit in any single at-bat is 0.300. Assuming that her chance of getting a hit on a particular time at bat is independent of her other times at bat, what is the probability that she will not get a hit until her fourth time at bat in a game

The probability that she will not get a hit until her fourth time at bat in a game is 0.103

Step-by-step explanation:

Previous concepts

The geometric distribution represents "the number of failures before you get a success in a series of Bernoulli trials. This discrete probability distribution is represented by the probability density function:"

Let X the random variable that measures the number os trials until the first success, we know that X follows this distribution:

Solution to the problem

For this case we want this probability

And using the probability mass function we got:

The probability that she will not get a hit until her fourth time at bat in a game is 0.103

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