Suppose there are 3 molecules in a container. If each molecule has a 1-in-2 chance of being in the left half of the container, what is the probability that there are exactly 2 molecules in the left half of the container?
A) 1/2
B) 1/3
C) 1/8
D) 3/8
E) 3/5

Question

Quizplus · Accepted Answer

There are a total of 2^3 = 8 possible arrangements for the molecules. We can use the binomial distribution to find the probability of exactly 2 molecules being in the left half of the container. The probability of a single molecule being in the left half is 1/2, and the probability of it being in the right half is also 1/2.
P(exactly 2 in left half) = (3 choose 2) * (1/2)^2 * (1/2)^1 = 3/8
Therefore, the answer is D).

Suppose There Are 3 Molecules in a Container