Question

According to a recent survey, 14% of the population owns a cat. 49 percent of cat owners are married, while 70% of non-cat owners are married. if you randomly select a person, what is the probability that she/he is married?

Answer 1

The probability that a randomly selected person is married is calculated using the total probability rule, considering both cat owners and non-cat owners in the population. The resulting probability is 67.06%.

Step-by-step explanation:

The question asks for the probability that a randomly selected person is married given the percentages of married cat owners and non-cat owners. To solve this, we need to use the total probability rule which combines the probability of both groups, taking into account the overall percentage of cat owners in the population.

Let's denote M as the event of being married, C as owning a cat, and N as not owning a cat. The problem states that P(M|C) = 0.49, P(M|N) = 0.70 and P(C) = 0.14. Since C and N are complementary events, P(N) = 1 - P(C) = 0.86.

Using the total probability rule:

P(M) = P(M|C)P(C) + P(M|N)P(N)
= 0.49 × 0.14 + 0.70 × 0.86
= 0.0686 + 0.602
= 0.6706 or 67.06%

Therefore, the probability that a randomly selected person is married is 67.06%.