Hardluck Harry has a batting average of .200 (i.e., a 20 percent chance of a hit each time he's at bat). Scouts for a rival baseball club secretly observe Harry's performance in 12 random times at bat. What is the probability that Harry will get more than 2 hits?
A).2055
B).2362
C).7946
D).4417

Question

Quizplus · Accepted Answer

To solve this problem, we need to use the binomial distribution formula, which is:
P(X > 2) = 1 - P(X ≤ 2) = 1 - [P(X=0) + P(X=1) + P(X=2)]

where X is the number of hits Harry gets in 12 at-bats, and P is the probability of getting X hits.

Using the binomial distribution formula, we can calculate the probability as follows:

P(X=0) = (0.8)^12 = 0.0687
P(X=1) = 12C1 * (0.2)^1 * (0.8)^11 = 0.2578
P(X=2) = 12C2 * (0.2)^2 * (0.8)^10 = 0.3570

Plugging these values into the equation above, we get:

P(X > 2) = 1 - (0.0687 + 0.2578 + 0.3570) = 0.3165

Therefore, the probability that Harry will get more than 2 hits in 12 at-bats is 0.3165, or about 31.65%. The closest answer choice is D, 0.4417, but this is not the correct answer.

Hardluck Harry Has a Batting Average of