Circuit boards are assembled by selecting 4 computer chips at random from a large batch of chips. In this batch of chips, 90 percent of the chips are acceptable. Let X denote the number of acceptable chips out of a sample of 4 chips from this batch. What is the least probable value of X?

the least probable value of X is X=0, with probability P (X=0) = 0.0001 = 0.01%

Step-by-step explanation:

denoting X=number of acceptable chips out of a sample of 4 chips. If the probability of choosing one acceptable chip is 0.90, then the probability of choosing one chip with failures is 1-0.90 = 0.1

since is less likely to take one failed chip (0.1 is smaller than 0.9), and each chip is independent from the others, the least probable value of X is when there are 4 failed chips or 0 acceptable chips. then the probability for P (X=0) will be

P (X=0) = 0.1*0.1*0.1*0.1 = 0.0001

Note:

Strictly speaking, X has a binomial distribution, therefore

P (X) = 4!/[ (4-x) !*x!]*0.9^x * 0.1^ (4-x)

that has a minimum value for X=0 → P (X=0) = 0.0001