A day can only be cloudy or sunny. The probability of a day being cloudy is…
2026
A day can only be cloudy or sunny. The probability of a day being cloudy is 0.5, independent of the condition on other days.
What is the probability that in any given four days, there will be three cloudy days and one sunny day?
- A.
1/4
- B.
3/4
- C.
2/3
- D.
3/8
Attempted by 3 students.
Show answer & explanation
Correct answer: A
Each day is independently cloudy with probability 1/2 and sunny with probability 1/2.
We need exactly 3 cloudy days and 1 sunny day in 4 days.
Choose the position of the sunny day: C(4,1) = 4 ways.
Probability of any one such sequence = (1/2)^4 = 1/16.
Required probability = 4 × 1/16 = 1/4.
Therefore, the probability is 1/4.
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