Two cards are drawn from a deck of 52 cards, with replacement. (This means that

Question

Two cards are drawn from a deck of 52 cards, with replacement. (This means that one person chooses a card, looks at it, and returns it, and then another person chooses a card, looks at it, and returns it.) Find the probability that: The first card is an ace and the second card is black. Both cards are spades. Neither card has a value from 2,3,4,5 At least one card is an ace. e. If the two cards are drawn without replacement (i.e., first card drawn out is not put back before drawing second card), find the probabilities of that both cards are spades.

Explanation / Answer

P(The first card is an ace and the second card is black) = (4/52)*(1/2) = 0.038

P(Both cards are spades) = (1/4)*(1/4) = 1/16 = 0.0625

P(Neither card has a value from 2,3,4,5) = (9/13)^2 =0.479  

P(At least one card is an ace) = 1- P(no Ace ) = 1- [(48/52)^2]= 0.0148

. e. If the two cards are drawn without replacement (i.e., first card drawn out is not put back before drawing second card), find the probabilities of that both cards are spades.

P = (13/52)*(12/51) = 0.059

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