Question

A fish tank contains 18 goldfish and 22 guppies. If you randomly select 2 fish, what is the probability that they are both goldfish?
a. 1/20
b. 51/260
c. 1/22
d. 1/36

Answer 1

The probability is the number of positive events divided by the number of total possible events. The probability searched will be the probability that the first fish selected is a goldfish times the probability that the second fish selected is also a goldfish. The probability that the first fish selected is a goldfish is the number of goldfish in the tank divided by the total number of fish, i.e. 18 / 40. The probality that the second fish selected is a goldfish is 17 / 39 (because there is one goldfish less in the thank). Then, the joint probability is (18/40)*(17/39) = 306/1560 =102/ 520 = 51/260. Then, the answer is the option b. 51/260