Question

Apple products have become a household name in America with 51% of all households owning at least one Apple product (CNN, March 19, 2012). The likelihood of owning an Apple product is 61% for households with kids and 48% for households without kids. Suppose there are 1,200 households in a representative community, of which 820 are with kids and the rest are without kids. Are the events "household with kids" and "household without kids" mutually exclusive and exhaustive?

Answer 1

Answer: It is mutually exclusive and exhaustive.

Explanation:

Since we have given that

Owns apple No apple Total

With kids 500.2 319.8 820

Without kids 182.4 197.6 380

Total 682.6 517.4 1200

P(Households without kids) =
`(380)/(1200)=0.316`

P(Households with kids) =
`(820)/(1200)=0.683`

And P(A∪B) = 0.316+0.683 = 0.999 ≈ 1

Since the two event are disjoint so, the probability of both occurring is 0 and the probability of either occurring is the sum of each occurring.

Hence, it is mutually exclusive and exhaustive.