Aptitude Day 147

Problems on Probability:

1. Two dices are tossed. The probability that the total score is not a prime number is:

Solution:

                 n(S) = 36.

                 n(E) ={(1,1),(1,2),(1,4),(1,6),(2,1),(2,3),(2,5),(3,2),(3,4),(4,1),(4,3),(5,2),(5,6),(6,1),(6,5)}

             

                  P(getting a prime number) = n(E)/ n(S)

                                                             = 15/36

                                                             = 5/12.

                                        

                 P(not getting a prime number) = 1-5/12

                                                                  = 7/12.

2. A speaks truth in 60% cases and B in 70% of the cases. In what percentage of cases are they likely to contradict each other, narrating the same incident?

Solution:

                P(A) =60/100 =3/5.

                P(A̅) = 1-3/5 = 2/5.

                P(B)=70/100 =7/10.

                P(B̅)= 1-7/10 =3/10

               Since they contradict each other while narrating the same incident. We get,

                           P(A)*P(B̅) + P(A̅)+P(B) = 3/5 * 3/10 + 2/5 * 7/10

                                                                   = 9/50 + 14/50

                                                                   = 23/50.

             The percentage will be (23/50) *(100) = 46%.