KCET2026MathematicsProbability
The probability that a man and his wife live after 20 years are 1 4 and 1 3 respectively. The probability that neither the man nor his wife live after 20 years is
Options
- A3 4
- B1 12
- C7 12
- D1 2
Correct answer
D. 1 2
Step-by-step solution
Let P(M) be the probability that the man lives after 20 years and P(W) be the probability that his wife lives after 20 years. Given P(M) = 1 4 and P(W) = 1 3 . The probability that the man does not live after 20 years is P( M ) = 1 - P(M) = 1 - 1 4 = 3 4 . The probability that the wife does not live after 20 years is P( W ) = 1 - P(W) = 1 - 1 3 = 2 3 . Assuming the events are independent, the probability that neither of them lives after 20 years is P( M W ) = P( M ) P( W ) . P( M W ) = 3 4 2 3 = 1 2 . Answer: 1 2