Question

A statistics problem is given to three students A, B, and C, whose chances of solving it are 1/3, 1/4, and 1/5 respectively. What is the probability that the problem is solved?

a) 2/3
b) 3/4
c) 2/5
d) 3/5

Answer 1

The probability that the statistics problem is solved by at least one of the three students is ¾.

Step-by-step explanation:

The question asks for the probability that a statistics problem is solved when given to three students A, B, and C with individual solving probabilities of ⅓, ⅔, and ⅕ respectively. To find the overall probability of the problem being solved, we calculate the probability that it is not solved by any of the students and subtract it from one. This utilizes the concept of complementary events in probability theory.

First, we find the probability that none of the students solve the problem:

P(A does not solve) = 1 - ⅓ = ⅓

P(B does not solve) = 1 - ⅔ = ¾

P(C does not solve) = 1 - ⅕ = ₄₅

Then, we multiply these probabilities to find the probability that none of them solve the problem:

P(A and B and C do not solve) = ⅓ * ¾ * ₄₅ = ⅚₌ₓ₏

Finally, the probability that at least one of them solves the problem is the complement of none solving:

P(at least one solves) = 1 - P(A and B and C do not solve) = 1 - ⅚₌ₓ₏ = ¾ (Option b)