A survey revealed that 21.5% of the households had no checking account,66.9% had regular checking accounts,and 11.6% had NOW accounts.Of those households with no checking account 40% had savings accounts.Of the households with regular checking accounts 71.6% had a savings account.Of the households with NOW accounts 79.3% had savings accounts. The probability that a randomly selected household has a savings account is:
A) 0.609.
B) 1.000.
C) 0.227.
D) 0.657.
E) 0.537.

Question

Quizplus · Accepted Answer

We can use the formula for total probability:

P(Savings) = P(Savings | No checking) * P(No checking) + P(Savings | Regular checking) * P(Regular checking) + P(Savings | NOW) * P(NOW)

Substituting in the given values:

P(Savings) = (0.40)(0.215) + (0.716)(0.669) + (0.793)(0.116)

P(Savings) = 0.086 + 0.479 + 0.091

P(Savings) = 0.657

Therefore, the probability that a randomly selected household has a savings account is 0.657, or choice D.

A Survey Revealed That 21