Forty-four percent of consumers with credit cards carry balances from month to month. Four consumers with credit cards are randomly selected. What is the probability that fewer than two consumers carry a credit card balance?
A) 0.4074
B) 0.6734
C) 0.7717
D) 0.3643

Question

Quizplus · Accepted Answer

The probability that fewer than two consumers carry a credit card balance can be calculated using the binomial probability formula. Let's denote the probability of carrying a balance as $p = 0.44$ and the probability of not carrying a balance as $q = 1 - p = 0.56$. We are interested in the cases where either 0 or 1 consumer carries a balance out of 4.For 0 consumers carrying a balance, the probability is $q^4 = 0.56^4$.For 1 consumer carrying a balance, the probability is $4 \times p \times q^3 = 4 \times 0.44 \times 0.56^3$.Adding these probabilities gives the total probability of fewer than two consumers carrying a balance:$$P(\text{fewer than 2}) = q^4 + 4pq^3 = 0.56^4 + 4 \times 0.44 \times 0.56^3 = 0.4074.$$Therefore, the correct answer is 0.4074, which corresponds to choice A.

Forty-Four Percent of Consumers with Credit Cards Carry Balances from Month