Probability topic

Question

A student appears at 3 exams. The Probability of passing of these exams are 1/5,1/6 and 1/7 .The Probability that of the passed in at least one exam

Answer 1

We could calculate the probability that the student passed exactly one exam, then add that to the probability that the student passed exactly two exams, then add that to the probability the student passed all three exams.

 

Or, we could calculate the probability that the student failed all three exams, then subtract that probability from 1. This method will work because the probability we are interested in is basically "the probability that the student did anything but fail all three exams." So, we'll find the probability he did fail all three exams, then find the probability that he did anything but that by subtracting from 1.

 

(Remember that all possible outcomes' probabilities for a given situation should add up to a total probability of 1. So, two events that together cover all possibilities, like "failed all exams" and "passed at least one exam," should have a combined probability of 1.)

 

 

 

P(Failed All Exams):

 

(4/5)(5/6)(6/7) = 4/7

 

 

P(Passed at Least One):

 

1 - 4/7 = 3/7