Question

question 4 of 28
elena is going to a farmers market for fresh produce. she has two markets to choose from and hopes to buy both cherries and asparagus. the table shows the probability that each type of produce will be available at the markets.

assuming that the availability of cherries and the availability of asparagus are independent of each other, which market should elena choose to maximize her chance of buying both?

a. south market. there is a 0.52 probability of both cherries and asparagus being available.
b. north market. there is a 0.48 probability of both cherries and asparagus being available.
c. north market. there is a 0.77 probability of both cherries and asparagus being available.
d. south market. there is a 0.77 probability of both cherries and asparagus being available.

Explanation:

Step1: Calculate probability for North market

Since the availability of cherries and asparagus are independent events, use the formula \(P(A\cap B)=P(A)\times P(B)\). For North market, \(P(\text{cherries}) = 0.96\) and \(P(\text{asparagus})=0.5\).
\(P(\text{North})=0.96\times0.5 = 0.48\)

Step2: Calculate probability for South market

For South market, \(P(\text{cherries}) = 0.8\) and \(P(\text{asparagus})=0.65\).
\(P(\text{South})=0.8\times0.65=0.52\)

Answer:

A. South market. There is a 0.52 probability of both cherries and asparagus being available.