Question

Rd from a pack of 52 playing cards is lost. from the remaining cards of the pack three cards are drawn at random (without replacement) and are found to be all spades. find the probability of the lost card being a spade

Answer 1

A= last card is spade

B= not spade

P(A)=1352=14P(A)=1352=14

P(B)=3952=34P(B)=3952=34

∈∈= 2 cards drawn are spade

P(∈A)=(1251)×(1150)=1322550P(∈A)=(1251)×(1150)=1322550

P(∈B)=(1351)×(1250)=1562550P(∈B)=(1351)×(1250)=1562550

P(A∈)=P(∈A)P(A)P(A)P(∈A)+P(∈B)P(B)P(A∈)=P(∈A)P(A)P(A)P(∈A)+P(∈B)P(B)

=1322550×141322550×4+156×32550×4=1322550×141322550×4+156×32550×4

=132132+468=132132+468

=132600=132600

=1150