Babe Ruth's lifetime betting averge was .343. In three times at bat, what is the prbability of the following?
a. he gets three hits
b. he gets no hits
c. he gets at least one hit.
d. he gets exactly one hit
Three hits: .343^3
no hits : (1-.343)^3 = .657^3
at least one hit: 1 - (1-.343)^3
exactly one hit: hmm, mhm, mmh
3(.343)(.657)^2
To calculate the probabilities, we need to understand a few things. Babe Ruth's lifetime betting average of .343 means he has a 34.3% chance of getting a hit in any given at-bat.
a. To find the probability of Babe Ruth getting three hits in three at-bats, we need to multiply the probability of getting a hit in a single at-bat three times.
Probability of getting a hit in a single at-bat = 0.343
Probability of getting three hits in three at-bats = 0.343 * 0.343 * 0.343 = 0.0417 (or 4.17%)
So, the probability of Babe Ruth getting three hits in three at-bats is approximately 4.17%.
b. To find the probability of Babe Ruth getting no hits in three at-bats, we need to find the probability of not getting a hit in a single at-bat and raise it to the power of three.
Probability of not getting a hit in a single at-bat = 1 - 0.343 = 0.657
Probability of getting no hits in three at-bats = 0.657 * 0.657 * 0.657 = 0.288 (or 28.8%)
So, the probability of Babe Ruth getting no hits in three at-bats is approximately 28.8%.
c. To find the probability of Babe Ruth getting at least one hit in three at-bats, we can subtract the probability of getting no hits from 1.
Probability of getting at least one hit = 1 - Probability of getting no hits
= 1 - 0.288
= 0.712 (or 71.2%)
So, the probability of Babe Ruth getting at least one hit in three at-bats is approximately 71.2%.
d. To find the probability of Babe Ruth getting exactly one hit in three at-bats, we need to calculate the probability of getting a hit in one at-bat and not getting a hit in the other two.
Probability of getting a hit = 0.343
Probability of not getting a hit = 1 - 0.343 = 0.657
Probability of getting exactly one hit in three at-bats = 0.343 * 0.657 * 0.657 = 0.146 (or approximately 14.6%)
So, the probability of Babe Ruth getting exactly one hit in three at-bats is approximately 14.6%.