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.