Question

Two cards are drawn, without replacement, from a standard 52-card deck. Find the probability of each of the following events: a) Both cards are red. b) Both cards are the same color. c) The second card is a queen, given that the first card is an ace.

Answer 1

Answer:

Step-by-step explanation:

given that two cards are  drawn, without replacement, from a standard 52-card deck.

a) Both cards are red

Here there are 26 red cards and 52 total cards.  

Probability = $\frac{26C2}{52C2} \\=\frac{26*25}{52*51} \\=\frac{25}{102}$

b) Both cards are the same color

i.e. either both are red or both are black

Hence probability = twice of part a

= $\frac{2*25}{102} \\=\frac{25}{51}$

c) The second card is a queen, given that the first card is an ace.

If first card is an ace remaining are 51 cards with 4 queens\

So prob = 4/51