Aptitude Day 140

Problems on Probability:

1. Two cards are drawn together from a pack of 52 cards. The probability that one is club and one is a diamond, is:

Solution:

                n(S) = ⁵²C2 = 1326

                n(E) = ¹³C1 *  ¹³C1 =  13*13 = 169.

                P(E) = n(E)/ n(S)

                         = 169/1326

                         = 13/102.

2. Two cards are drawn from a pack of 52 cards. The probability that either both are black or both are Queens, is:

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.