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Sagot :
To determine which market Elena should choose to maximize her chance of buying both cherries and asparagus, let's analyze the probabilities given in the table and calculate the chances for both markets.
1. Calculate the probability that both cherries and asparagus are available at the North market:
- Probability of cherries being available at the North market: [tex]\( P(\text{Cherries}_{North}) = 0.6 \)[/tex]
- Probability of asparagus being available at the North market: [tex]\( P(\text{Asparagus}_{North}) = 0.85 \)[/tex]
- Since the availability of cherries and asparagus are independent events, the probability that both are available at the North market is:
[tex]\[ P(\text{Both}_{North}) = P(\text{Cherries}_{North}) \times P(\text{Asparagus}_{North}) = 0.6 \times 0.85 = 0.51 \][/tex]
2. Calculate the probability that both cherries and asparagus are available at the South market:
- Probability of cherries being available at the South market: [tex]\( P(\text{Cherries}_{South}) = 0.5 \)[/tex]
- Probability of asparagus being available at the South market: [tex]\( P(\text{Asparagus}_{South}) = 0.84 \)[/tex]
- Similarly, the probability that both are available at the South market is:
[tex]\[ P(\text{Both}_{South}) = P(\text{Cherries}_{South}) \times P(\text{Asparagus}_{South}) = 0.5 \times 0.84 = 0.42 \][/tex]
3. Compare the probabilities:
- North market: [tex]\( P(\text{Both}_{North}) = 0.51 \)[/tex]
- South market: [tex]\( P(\text{Both}_{South}) = 0.42 \)[/tex]
Since [tex]\( 0.51 > 0.42 \)[/tex], the probability of both cherries and asparagus being available is higher at the North market.
Therefore, Elena should choose the North market to maximize her chance of buying both cherries and asparagus. The correct answer is:
A. North market. There is a 0.51 probability of both cherries and asparagus being available.
1. Calculate the probability that both cherries and asparagus are available at the North market:
- Probability of cherries being available at the North market: [tex]\( P(\text{Cherries}_{North}) = 0.6 \)[/tex]
- Probability of asparagus being available at the North market: [tex]\( P(\text{Asparagus}_{North}) = 0.85 \)[/tex]
- Since the availability of cherries and asparagus are independent events, the probability that both are available at the North market is:
[tex]\[ P(\text{Both}_{North}) = P(\text{Cherries}_{North}) \times P(\text{Asparagus}_{North}) = 0.6 \times 0.85 = 0.51 \][/tex]
2. Calculate the probability that both cherries and asparagus are available at the South market:
- Probability of cherries being available at the South market: [tex]\( P(\text{Cherries}_{South}) = 0.5 \)[/tex]
- Probability of asparagus being available at the South market: [tex]\( P(\text{Asparagus}_{South}) = 0.84 \)[/tex]
- Similarly, the probability that both are available at the South market is:
[tex]\[ P(\text{Both}_{South}) = P(\text{Cherries}_{South}) \times P(\text{Asparagus}_{South}) = 0.5 \times 0.84 = 0.42 \][/tex]
3. Compare the probabilities:
- North market: [tex]\( P(\text{Both}_{North}) = 0.51 \)[/tex]
- South market: [tex]\( P(\text{Both}_{South}) = 0.42 \)[/tex]
Since [tex]\( 0.51 > 0.42 \)[/tex], the probability of both cherries and asparagus being available is higher at the North market.
Therefore, Elena should choose the North market to maximize her chance of buying both cherries and asparagus. The correct answer is:
A. North market. There is a 0.51 probability of both cherries and asparagus being available.
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