Find the probability that exactly two cells remain empty

Question

Twenty balls are placed random into four cells. Find the probability that exactly two cells remain empty

Answer 1

Hello Catherine,

In this problem, what matters is the number of cells not the number of balls. Regardless, of the number of balls that are randomly placed, each cell will either be empty or not. Hence by the fundamental counting principle there will be a total of 2^4 = 16 possible outcomes. Next, we need to determine the number of outcomes that result in two empty cells. This can be done by listing these outcomes as follows:

Let E = empty and N=nonempty

{EENN, ENEN, ENNE, NEEN, NENE, NNEE}

Hence the probability that exactly two cells remain empty is given by,

P(two empty cells) = (number of outcomes with two empty cells) / (total number of possible outcomes)

P(two empty cells) = 6/16 = 3/8 = 0.375