# 11.4.1. Calculating Probability

40 rats were injected with a poisonous substance, and the number of dead rats is observed within 12 hours. If the probability that at most 24 rats will die is , and the probability that exactly 24 rats will die is , determine the probability that at least 24 rats will die.

• A0.65
• B0.9
• C0.55
• D0.35

### Example

40 rats were injected with a poisonous substance, and the number of dead rats is observed within 12 hours. If the probability that at most 24 rats will die is , and the probability that exactly 24 rats will die is , determine the probability that at least 24 rats will die.

### Solution

In this case, event is at most 24 rats dying, and event is at least 24 rats dying. The notation refers to the probability of either event or event occurring, or both. Since event occurring, event occurring, and both occurring are the only three possibilities in the sample space in this case, must be equal to 1. If and are two non-mutually exclusive events, then where the notation refers to the probability of events and occurring together. Use this fact to find the probability of .

Thus, the probability that at least 24 rats will die is 0.65.

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