A card is drawn from a regualr deck of 52 cards and is then

A card is drawn from a regualr deck of 52 cards and is then put back in the deck. A second card is drawn. What is the probability that:

THe first card is red-

The second card is hearts given that the first is red

The first card is red and the second is hearts

Solution

a)

There are 26 red cards out of 52.

Hence

P(red) = 26/52 = 1/2 = 0.5 [answer]

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b)

The second card is independent of the first card, as the first card is replaced.

Thus, as there are 13 hearts,

P(2nd is hearts) = P(hearts) = 13/52 = 1/4 = 0.25 [answer]

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c)

As they are independent, the probability of their intersection is the product of their probabilities,

P(first is red, second is hearts) = (1/2)(1/4) = 1/8 = 0.125 [answer]