A card from a pack of 52 playing cards is lost. From the remaining car

1.	A card from a pack of 52 playing cards is lost. From the remaining cards of the Packthree 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» A= lost card is spade B= not spade P(A)=13/52=1/4 P(B)=39/52=3/4 Let E be three cards drawn which is spade P(E/A)=12/5111/5010/49=1320/124950=0.0105 P(E/B)=13/5112/5011/49=1716/124950=0.013 P(A/E)=P(E/A)P(A)/[P(A)P(E/A)+P(E/B)P(B)] =0.01051/4/[1/40.0105+0.013*3/4]=0.0729

A card from a pack of 52 playing cards is lost. From the remaining cards of the Packthree 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»

A= lost card is spade

B= not spade

P(A)=13/52=1/4

P(B)=39/52=3/4

Let E be three cards drawn which is spade

P(E/A)=12/51*11/50*10/49=1320/124950=0.0105

P(E/B)=13/51*12/50*11/49=1716/124950=0.013

P(A/E)=P(E/A)P(A)/[P(A)*P(E/A)+P(E/B)*P(B)]

=0.0105*1/4/[1/4*0.0105+0.013*3/4]=0.0729