Question

A problem in mathematics is given to three students A, B and C whose chance of...

A problem in mathematics is given to three students A, B and C whose chance of solving it are 1/2 , 1/3 ??? 1/4 . Find the probability that (i) None of the students solves the problem (ii) All the three students solves the problem (iii) Exactly one of them solves the problem (iv) Any two of them solves the problem

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Answer:

a)

b)

1/2*1/3*1/4 = 1/24

c)

We have to do it for each student

=> 1/2*2/3*3/4 + 1/2*1/3*3/4+ 1/2*2/3*1/4

= 6/24 + 3/24 + 2/24 = 11/24

d)

There are 3 combinations which we have to consider

= 1/2*1/3*3/4 + 1/2*1/3*1/4 + 1/2*2/3*1/4

= 3/24 + 1/24 + 2/24 = 6/24 = 1/4

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