Question

For each time up at bat, a baseball player has a 70% chance of making an out, a 10% chance of getting walked, and a 20% chance of getting a hit. Estimate the probability that, out of 5 at-bats, the player gets at least one hit. Use 40 simulation runs.

Can you please help solve, with step by step

1

Answer 1

Answer:

Given,

Let A be an occasion meaning that the player gets a hit.

i.e.,

P(A) = 0.20

In this way A ~ Bernoulli(0.20)

Let us assume that A1, A2, A3, ... A5 indicate that the player gets a hit in 5 at-bats.

where as

Ai 's are autonomous of one another and they are additionally indistinguishably appropriated as Bernoulli (0.20).

In this manner S = Ai (whereas i = 1 to 5) = Bin(5.0.2) as the entirety of Bernoulli variates pursue a Binomial distribution.

Here S signifies the quantity of hits out of 5 at-bats.

In this manner the required probability can be given as follows

i.e.,

P(S >= 1) = 1 - P(S=0)

P(S = 0) = (1 - P(A))^5

= (1 - 0.20)^5

P(S = 0) = 0.32768

In this manner the required probability is 1 - 0.32768

= 0.67232 is the required probability of getting at least one hit.

Hence required probability = 0.67232