Question

A card is drawn from a regular deck of 52 cards and is then put back in the deck. A second card is drawn. What is the probability that:
(a) The first card is red.
(b) The second card is hearts given that the first is red.
(c) The first card is red and the second is hearts.

Answer 1

Answer:

0.5,0.25,0.125

Step-by-step explanation:

Given that a card is drawn from a regular deck of 52 cards and is then put back in the deck. A second card is drawn.

Since here we have the draws with replacement we can say each trial is independent of the other.

i.e. the first card does not affect the second card at all.

the probability that:

a) The first card is red.

=$\frac{26}{52} =0.50$

(b) The second card is hearts given that the first is red.

=P(second is hearts)

= 0.25

(c) The first card is red and the second is hearts.

= $0.5*0.25\\=0.125$

(since independent)