Question

A card is drawn from a 52 card deck; then a second card is drawn; then a third card is drawn. Find the probability of getting two queens and then an ace.

a) With replacement?

b) Without replacement ?

Answer 1

A card is drawn from a 52 card deck; then a second card is drawn; then a third card is drawn. Find the probability of getting two queens and then an ace.

a) With replacement?

P[ getting two queens and then an ace ] = P[ drawing a queen ]*P[ drawing a queen ]*P[ drawing a ace ]

P[ getting two queens and then an ace ] = (1/13)*(1/13)*(1/13)

P[ getting two queens and then an ace ] = 1/2197

b) Without replacement ?

P[ getting two queens and then an ace ] = P[ drawing two queen ]*P[ drawing a ace ]

P[ getting two queens and then an ace ] = (1/13)*(3/51)*(4/50)

P[ getting two queens and then an ace ] = (1/13)*(1/17)*(2/25)

P[ getting two queens and then an ace ] = 2/5525