To determine whether the probability that a customer either orders a steak or has an alcoholic beverage is equal to 0.25 + 0.32 = 0.57, we need to examine if these two events are mutually exclusive.
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Definition of Mutually Exclusive Events: Two events are mutually exclusive if they cannot occur at the same time. That is, if one event happens, the other cannot.
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Given Probabilities:
- Probability of ordering a steak \( P(S) = 0.25 \)
- Probability of having an alcoholic beverage \( P(A) = 0.32 \)
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Calculation of Combined Probability: If the two events are mutually exclusive, we can simply add the probabilities: \[ P(S \cup A) = P(S) + P(A) = 0.25 + 0.32 = 0.57 \]
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Checking for Overlap: However, if ordering a steak and having an alcoholic beverage are not mutually exclusive (i.e., a customer can do both), we would need to subtract the probability of both occurring together: \[ P(S \cup A) = P(S) + P(A) - P(S \cap A) \]
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Conclusion: Without additional information regarding customers who order both steak and an alcoholic beverage, we cannot definitively state that they are mutually exclusive. Therefore, unless we know that these two events do not overlap, we cannot conclude that the probability is simply 0.57.
So, to finish your statement:
The probability that a customer either orders a steak or has an alcoholic beverage is not equal to 0.25 + 0.32 = 0.57 because the two events are not mutually exclusive unless further information specifies that they do not occur together.