Question

Given:  A regular deck of 52 cards.   Cards are drawn without replacement.  R = red card; B = black card; C = club; D = diamond; H = heart; S = spade; J = Jack; Q = Queen; K = King; A = Ace.

19.  P(S) = 13/52                   20.  P(Q and Q) =                        21.  P(Q and J) =                                                                                                                                                                                         22.  P(H and D) =. 23.  P(Q | Q) =               24.  P(R | R) =                         25.  P(R | B) =                                                                                                                                                                                       26.  P(A | K)=

27.  What is the probability that the card is red if it is known to be a diamond?

28.  What is the probability that the card is a diamond if it is known to be red?

29.  What is the probability that the card is an ace if it is known to be a club?

30.  What is the probability that the card is a club if it is known to be a jack?

Answer 1

(as per policy i will answer first 4 parts : 19,20,21,22)

19.  P(S)

P(S) = no. of spades / no. of cards

= 13/52 = 0.25

20.  P(Q and Q)

P(Q and Q) = (choose 2 queens out 4 total queens)/(choose 2 cards from 52 cards)

= 4C2 / 52C2

= 6 / 1326

= 0.0045

21.  P(Q and J)

= ( (choose 1 queen out 4 total queens)*(choose 1 Jack out 4 total jacks) )/(choose 2 cards from 52 cards)

= 4C1 * 4C1 / 52C2

=4*4 / 1326

= 0.0121

22.  P(H and D)

= ( (choose 1 heart out 13 total hearts)*(choose 1 diamond out 13 total diamonds) )/(choose 2 cards from 52 cards)

= 13C1 * 13C1 / 52C2

= 13*13 / 1326

= 0.1275

(please UPVOTE)