To solve this problem, we need to find the probability that at least one of the students solves the problem. This is equivalent to finding the probability that not all of them fail to solve the problem.

Step 1: Find the probability that each student fails to solve the problem.

For the first student, the probability of failure is 1 - 1/2 = 1/2.
For the second student, the probability of failure is 1 - 1/3 = 2/3.
For the third student, the probability of failure is 1 - 1/4 = 3/4.

Step 2: Find the probability that all students fail.

The probability that all events occur is the product of their individual probabilities. So, the probability that all students fail is (1/2) * (2/3) * (3/4) = 1/4.

Step 3: Find the probability that at least one student succeeds.

The probability that at least one student succeeds is the complement of the probability that all students fail. So, the probability that the problem is solved is 1 - 1/4 = 3/4.

So, the probability that the problem will be solved is 3/4.

Question

To solve this problem, we need to find the probability that at least one of the students solves the problem. This is equivalent to finding the probability that not all of them fail to solve the problem.

Step 1: Find the probability that each student fails to solve the problem.

For the first student, the probability of failure is 1 - 1/2 = 1/2.
For the second student, the probability of failure is 1 - 1/3 = 2/3.
For the third student, the probability of failure is 1 - 1/4 = 3/4.

Step 2: Find the probability that all students fail.

The probability that all events occur is the product of their individual probabilities. So, the probability that all students fail is (1/2) * (2/3) * (3/4) = 1/4.

Step 3: Find the probability that at least one student succeeds.

The probability that at least one student succeeds is the complement of the probability that all students fail. So, the probability that the problem is solved is 1 - 1/4 = 3/4.

So, the probability that the problem will be solved is 3/4.

Knowee AI · Accepted Answer

To solve this problem, we need to find the probability that at least one of the students solves the problem. This is equivalent to finding the probability that not all of them fail to solve the problem.

Step 1: Find the probability that each student fails to solve the problem.

For the first student, the probability of failure is 1 - 1/2 = 1/2.
For the second student, the probability of failure is 1 - 1/3 = 2/3.
For the third student, the probability of failure is 1 - 1/4 = 3/4.

Step 2: Find the probability that all students fail.

The probability that all events occur is the product of their individual probabilities. So, the probability that all students fail is (1/2) * (2/3) * (3/4) = 1/4.

Step 3: Find the probability that at least one student succeeds.

The probability that at least one student succeeds is the complement of the probability that all students fail. So, the probability that the problem is solved is 1 - 1/4 = 3/4.

So, the probability that the problem will be solved is 3/4.

A problem is given to three students whose chances of solving it are 1/2, 1/3and ¼ respectively. What is the probability that the problem will be solved?

Question

A problem is given to three students whose chances of solving it are $\frac{1}{2}$ , $\frac{1}{3}$ , and $\frac{1}{4}$ respectively. What is the probability that the problem will be solved?

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