Question

The probability of A solving a riddle is 45 and that of B solving it is 23. Find the probability that the problem will not be solved at all.

a. 15/91
b. 4/90
c. 1/15
d. 1/9

Answer 1

The probability that neither A nor B solves the riddle is
`\( (1)/(15) \)`, which matches option C.

If the probability of A solving the riddle is
`\( P(A) = (4)/(5) \)` and the probability of B solving the riddle is
`\( P(B) = (2)/(3) \)`, then the probability that neither A nor B solves the riddle is indeed given by:

`\[ P(\overline{A} \cap \overline{B}) = P(\overline{A}) \cdot P(\overline{B}) \]`

Where
`\( P(\overline{A}) \)` is the probability that A does not solve the riddle, and
`\( P(\overline{B}) \)` is the probability that B does not solve the riddle.

`\[ P(\overline{A}) = 1 - P(A) = 1 - (4)/(5) = (1)/(5) \]\[ P(\overline{B}) = 1 - P(B) = 1 - (2)/(3) = (1)/(3) \]`

Now, multiply these probabilities:

`\[ P(\overline{A} \cap \overline{B}) = (1)/(5) \cdot (1)/(3) = (1)/(15) \]`

Option C is the correct answer.

The complete question is:

The probability of A solving a riddle is 4/5 and that of B solving it is 2/3. Find the probability that the problem will not be solved at all.

a. 15/91

b. 4/90

c. 1/15

d. 1/9