Answer:
The probability that Mark will have fewer than 3 hits in his next 6 at bats is approximately 0.204.
Explanation:
A batting average is the number of hits a player has divided by the number of times they have been at bat. In this case, Mark has a batting average of 0.155, which means that he has hit 0.155 of the times he has been at bat.
To find the probability that Mark will have fewer than 3 hits in his next 6 at bats, we can use the binomial probability formula. The formula for binomial probability is:
P(x) = (n choose x) * p^x * (1-p)^(n-x)
Where "n" is the number of trials, "x" is the number of successes, "p" is the probability of success on a single trial, and "1-p" is the probability of failure on a single trial.
In this case, the number of trials is 6, the number of successes is 3, and the probability of success on a single trial is 0.155. Plugging these values into the formula, we get:
P(3) = (6 choose 3) * 0.155^3 * (1-0.155)^(6-3)
To calculate the probability that Mark will have fewer than 3 hits in his next 6 at bats, we need to sum the probabilities of 0, 1, and 2 hits. We can use the binomial probability formula to calculate the probability of each of these outcomes, and then add them together to find the total probability.
For 0 hits, the probability is:
P(0) = (6 choose 0) * 0.155^0 * (1-0.155)^(6-0) = 0.009
For 1 hit, the probability is:
P(1) = (6 choose 1) * 0.155^1 * (1-0.155)^(6-1) = 0.054
For 2 hits, the probability is:
P(2) = (6 choose 2) * 0.155^2 * (1-0.155)^(6-2) = 0.141
Adding these probabilities together, we get the total probability that Mark will have fewer than 3 hits in his next 6 at bats:
P(0 or 1 or 2) = 0.009 + 0.054 + 0.141 = 0.204
Therefore, the probability that Mark will have fewer than 3 hits in his next 6 at bats is approximately 0.204.