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Let X be the number of students who show up for a professor's office hour on a particular day, pmf of X is p(0) = 0.10, p(1) = 0.20, p(2) = 0.25, p(3) = 0.30 and p(4) = 0.15, what is the probability at least 2 students show up? I tried doing P(p(1) u p(2)) = P(p(1)) + P(p(2)) - (P(p(1) n p(2))) what would be the correct formula?



Answer :

The probability at least 2 students show up is .70 or 70%

Let X be the number of students who show up for a professor's office hour on a particular day, probability of X is p(0) = 0.10, p(1) = 0.20, p(2) = 0.25, p(3) = 0.30 and p(4) = 0.15

If we add the probability of 1 student to show up , 2 student to show up, 3 student to show up and 4 student to show up

We get 0.10+ 0.20+ 0.25+ 0.15 =1

As the sum of these individual 4 possibilities is 1 that means these are the only possibilities  to exit

Now we need to find out  the probability at least 2 students show up which means probability of two or more students to show up

Which ca be written as

            p(≥2) = p(2) + p(3) + p(4)

            p(≥ 2) = 0.25+0.30+0.15

           p(≥2) = 0.70

Hence, the probability at least 2 students show up is .70 or 70%

To know more about probability  - https://brainly.com/question/11234923

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