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Aptitude Day 146

Problems on Probability:

1. A box contains 10 electric bulbs, out of which 3 is defective. 2 bulbs are chosen at random from this box. The probability that at least one of these is defective, is:

Solution:
                 n(S) = 10C2 =  45

                  n(E) = 7C2  = 21.
                      
                  P(none is defective) = n(E)/ n(S)
                                                   = 21/45
                                                   = 7/15.

                  P(at least one is defective) = 1- 7/15
                                                             = 8/15.

2. In class, 40% of the students English, 30% offered French and 20% offered both. If a student is selected at random. What’s the probability that he has offered both English and French?

Solution:
                 P(AUB) = P(A)+P(B)-P(A∩B)
                               = 40/100+30/100-20/100
                               = 50/100
                               = 1/2.

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