Answer:
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
