# 11.4.1. Calculating Probability

If the probability that a student succeeds in one of two subjects at least is 0.9, determine the probability that he fails in the two subjects.

• A0.1
• B0.9
• C0.45
• D0.55

### Example

The probability that a student succeeds in mathematics is 0.72, and the probability that he fails in physics is 0.28, while the probability that he succeeds in one of the two subjects at least is 0.76. Determine the probability that he fails in the two subjects.

### Solution

In this case, event is the student succeeding in mathematics, and event is the student succeeding in physics. The notation refers to the probability of either event or event occurring, or both. In other words, the notation refers to the probability of at least one of the events occurring. Since and are complementary, the sum of their probabilities is equal to 1. Use this fact to find the probability of .

Thus, the probability that the student fails in the two subjects is 0.24.

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