Question

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

Answer 1

Probability helps us to know the chances of an event occurring. The probability that the problem will be solved is 3/4.

What is Probability?

Probability helps us to know the chances of an event occurring. The sum of all the probabilities of an event is always equal to 1. The formula for probability is given as,

$\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}$

Let the three students be named A, B, and C with probabilities as 1/2, 1/3, and 1/4, respectively.

Now, the sum of all the probabilities of an event is 1. Therefore, we can write,

The Probability that A can not do it = 1 - Probability that A can do it

                                                      = 1 - 1/2

                                                      = 1/2

The probability that B can not do it = 1 - Probability that B can do it

                                                     = 1 - 1/3

                                                      = 2/3

​

The probability that C can not do it = 1 - Probability that C can do it

                                                     = 1 - 1/4

                                                      = 3/4

Now, if any of these solves the problem, the problem is solved. As a result, we may write,

∴P (at  least one of them solves the problem) = 1− probability none of them can solve the problem or

P(A∪B∪C) = 1 − [(1/2)(2/3)(3/4)]

               = 1 - 1/4

               = 3/4

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

Learn more about Probability here:

brainly.com/question/795909

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