Question

Three defective electric toothbrushes were accidentally shipped to a drugstore by Fresh

Answer 1

 When you are sampling from a small finite lot, the hypergeometric distribution applies. The binomial is a poor approximation in this case. 
The general equation for the hypergeometric where aCx means the number of combinations of a items selected x at-a-time.: 
P(x) =[(aCx)(N-aCn-x)]/NCn 
Where 
N is the lot size = 20 
a is the number of defectives in the lot = 3. 
x is the number of defectives in the sample. 
n is the sample size = 2. 
A. The probability that the first item is defective is 
P(x=1) = [(3C1)(17C1)]/(20C2) 
= (3)(17)/190 = 0.268 
The probability that the second item is defective is 
P(x = 1) = [(2C1)(17C1)]/(19C2) = (2)(17)/171 = 0.199. 
So the total probability is (0.268)(0.199) = 0.0532 
B. The probability that the first item is good is: 
P(x = 0) = (3C0)(16C2)]/20C2 = (1)(120)/190 = 0.632 
The probability that the second item is defective is 
P(x = 0) =[(3C0)(16C2)]/19C2 
= (1)(120)/171 = 0.670. 
The total probability is 0.632(0.670) = 0.4234