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. Let event A correspond to "Household with kids", and B to "Household owns an Apple product". a. Are the events "household with kids" and "household without kids" mutually exclusive and exhaustive? Yes No b. What is the probability that a household is without kids? (Round your answer to 4 decimal places.) c. What is the probability that a household is with kids and owns an Apple product? (Do not round intermediate calculations. Round your answer to 4 decimal places.) d. What is the probability that a household is without kids and does not own an Apple product? (Do not round intermediate calculations. Round your answer to 4 decimal places.)

Answer 1

Answer:

a. Yes.

b. The probability that a household is without kids:

= 0.3167

c. The probability of a household is with kids and owns an Apple product:

= 61%

d. The probability that a household is without kids and does not own an Apple product:

= 52%

Step-by-step explanation:

a) Data and Calculations:

Probability of a household owning an Apple product = 51%

This implies that the probability of a household not owning an Apple product = 49% (100 - 51)%.

Probability of a household with kids owning an Apple product = 61%

This implies that the probability of a household with kids not owning an Apple product = 39% (100 - 61)%.

Probability of a household without kids owning an Apple product = 48%

This also implies that a household without kids not owning an Apple product = 52% (100 - 48)%.

Sample of households = 1,200

Households with kids = 820

Probability of households with kids = 0.6833 (820/1,200)

Therefore, the probability of households without kids = 0.3167 (380/1200)

b) The events "household with kids" and "household without kids" are mutually exclusive and exhaustive because (a) the two events are separate and do not overlap and (b) the two events are inclusive of all possible options.  It is either a household has kids or it does not.  In this situation, no middle ground exists.