Two cards are selected without replacement from a usual deck of 52 cards. [A dec

Question

Two cards are selected without replacement from a usual deck of 52 cards. [A deck of cards has four suits (hearts, diamonds, spades, clubs) and each suit has 13 cards (2 to 10, J, Q, K, A).] using a probability tree

(a) Find the following probabilities:

(i) both cards are aces

(ii) both cards are spades

(iii) both cards are aces but neither is the ace of spades

(iv) one card is an ace and the other is a king

(v) one of the cards is the ace of spades

(vi) at least one of the cards is a spade or a face card (J, Q, K)

(vii) exactly one of the cards is a jack.

(b) If both cards selected were face cards, what is the probability both were queens?

Explanation / Answer

a) Both Aces = 4C2/52C = 4*3/[52*51] = 12/2652

b) Both spades = 13C2/52C2 = 156/2652

c) Both aces but not ace of spaded = 3C2 /52C2 = 6/2652

d) One ace and one king = 4C1 *4C1/52C2 = 16*2/2652 = 32/2652

Plase post the rest indiviudally.

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