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.

Step-by-step 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) = $\dfrac{380}{1200}=0.316$

P(Households with kids) = $\dfrac{820}{1200}=0.683$

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.