The probability that it will rain today is 0.5. The probability that it will…

1997

The probability that it will rain today is 0.5. The probability that it will rain tomorrow is 0.6. The probability that it will rain either today or tomorrow is 0.7. What is the probability that it will rain today and tomorrow?

  1. A.

    0.3

  2. B.

    0.25

  3. C.

    0.35

  4. D.

    0.4

Attempted by 6 students.

Show answer & explanation

Correct answer: D

Let A be the event that it rains today and B be the event that it rains tomorrow.

Given:
P(A) = 0.5, P(B) = 0.6, and P(A ∪ B) = 0.7.

Using the addition rule,
P(A ∪ B) = P(A) + P(B) - P(A ∩ B).

So,
0.7 = 0.5 + 0.6 - P(A ∩ B)
P(A ∩ B) = 1.1 - 0.7 = 0.4.

Therefore, the probability that it will rain both today and tomorrow is 0.4.

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