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Four person independently solve a certai...

Four person independently solve a certain problem correctly with probabilities `1/2,3/4,1/4,1/8dot` Then the probability that he problem is solve correctly by at least one of them is `(235)/(256)` b. `(21)/(256)` c. `3/(256)` d. `(253)/(256)`

A

`235/256`

B

`21/256`

C

`3/256`

D

`253/256`

Text Solution

AI Generated Solution

To solve the problem, we need to find the probability that at least one of the four persons solves the problem correctly. We can use the complement rule, which states that the probability of at least one event occurring is equal to 1 minus the probability of none of the events occurring. ### Step-by-Step Solution: 1. **Identify the probabilities of each person solving the problem correctly:** - Let \( P(A) = \frac{1}{2} \) (Probability that person A solves it) - Let \( P(B) = \frac{3}{4} \) (Probability that person B solves it) - Let \( P(C) = \frac{1}{4} \) (Probability that person C solves it) ...
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