Hello,nikk!

From a pack of 52 playing card, two card are selected without replacement.

What is the probability that:

(a) both cards are Diamonds? (ans: 1/17)

The first card must be a Diamond: .probability =

. . There are 13 Diamonds among the 52 cards.

The second card must be a Diamond: .probability =

. . There are 12 remaining Diamonds among the remaining 51 cards.

Therefore: .

(b) both cards are same suit ? (ans: 4/17)

The first card can be ANY card: .

The second card must match that suit: .

. . There are 12 remaining cards of that suit.

Therefore: .

There are two cases to consider . . .(c) one card is a Spade and the other a Club? (ans: 13/102)

(1) The first is a Spade: .

. . .The second is a Club: .

(2) The first is a Club: .

. . .The second is a Spade: .

Therefore: .

(d) both cards are different suits? (ans: 13/17)

The first card can be ANY card: .

The second card mustnotmatch the first: .

. . There are 39 cards of another suit among the 51 remaining cards.

Therefore: .