Question

Take two cards from a deck withoutreplacement. What is the probability of getting a red queen and then another red card?

Answer 1

Solution:

Given: Take two cards from a deck without replacement.

Find:

P(  getting a red queen and then another red card) =.............?

P( Red Queen and Another any Red card) =.................?

P( Red Queen and Another any Red card) = P( Red Queen) X P( Another any Red card)

We have 4 cards of Queen out of which two are Red

and there are total 26 red cards in 52 playing cards.

thus a red queen card can be selected in 2 ways

and for second draw, we have 26-1 = 25 red cards

thus

P( Red Queen and Another any Red card) = P( Red Queen) X P( Another any Red card)

P( Red Queen and Another any Red card) = ( 2 /52 ) X ( 25 / 51)

Here number is reduced by 1 , since we are not replacing card.

P( Red Queen and Another any Red card) =  0.0384615 X 0.4901961

P( Red Queen and Another any Red card) = 0.0188537

P( Red Queen and Another any Red card) = 0.018854

_{(Round final answer to specified number of decimal places)}