Aptitude Day 130

Problems on Probability:

1. 2 dices are thrown together. What’s the probability that the sum of the numbers on the 2 faces is divisible by 3 or 5?

Solution:

                 n(S) = 36.

                

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

               n(E) = 19

               P(E) = n(E)/ n(S)

                       = 19/36.

2. 2 cards are drawn at random from a pack of 52 cards. What’s the probability that either both are red or both are kings?

Solution:

                 n(S) = ⁵²C2 = 52*51/ 1*2 = 1326.

                 P(AUB) = P(A)+ P(B) – P(A∩B)

                n(A) = ²⁶C2 = 325.

                n(B) = ⁴C2 = 6

                n(A∩B) = ²C2 = 1

                 P(A) = n(A) / n(S) =  325/1326.

                 P(B) = n(B) / n(S) =  6/1326.

                 P(A∩B) = n(A∩B) / n(S) =  1/1326.

                Substitute all these 3 equations in the above equation. We get,

                P(AUB) = 325/1326 +6/1326 – 1/1326

                              = 330/1326

                              = 55/221.