apple products have become a household name in america. suppose that the likelihood of owning an apple…

apple products have become a household name in america. suppose that the likelihood of owning an apple product is 71% for households with kids and 55% for households without kids. suppose there are 1,270 households in a representative community, of which 880 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? note: round your answer to 4 decimal places. probability 0.7000 c. what is the probability that a household is with kids and owns an apple product? note: do not round intermediate calculations. round your answer to 4 decimal places. p(a ∩ b) 0.3000

apple products have become a household name in america. suppose that the likelihood of owning an apple product is 71% for households with kids and 55% for households without kids. suppose there are 1,270 households in a representative community, of which 880 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? note: round your answer to 4 decimal places. probability 0.7000 c. what is the probability that a household is with kids and owns an apple product? note: do not round intermediate calculations. round your answer to 4 decimal places. p(a ∩ b) 0.3000

Answer

Explanation:

Step1: Define mutually - exclusive and exhaustive

A household cannot have kids and not have kids at the same time, so the events are mutually exclusive. Also, a household either has kids or does not have kids, covering all possible cases, so they are exhaustive.

Step2: Calculate probability of household without kids

The number of households with kids is 880 and the total number of households is 1270. The number of households without kids is $1270 - 880=390$. The probability $P(\text{without kids})=\frac{390}{1270}\approx0.3071$.

Step3: Calculate probability of household with kids and owns Apple product

The probability of a household having kids is $P(A)=\frac{880}{1270}$. The probability of a household with kids owning an Apple product is 0.71. By the multiplication rule of probability for dependent events $P(A\cap B)=P(A)\times P(B|A)$. Here $P(A)=\frac{880}{1270}$ and $P(B|A) = 0.71$, so $P(A\cap B)=\frac{880}{1270}\times0.71\approx0.4913$.

Answer:

a. Yes b. 0.3071 c. 0.4913