Please every step in the calculation If you draw two cards a

Please every step in the calculation

If you draw two cards at random (without replacement) from a standard deck of 52 playing cards, what is the probability that:

(a) One will be red and one will be black?

(b) Both cards are spades?

Solution

a) There are two types of colors: black and red.

The probability of having a red or a black card among 52 cards: 26/52 or 1/2.

On the first draw, the probability of either of them = 26/52 or 1/2

On second draw, the probability of the other color = 26/51

Total probability = 1/2 * 26/ 51 or 26/102 or 13/ 51 or 0.2549

2) On first draw, the probability of having a spade among 52 cards: 13/52 or 1/4.

On second draw, the probability of having other spade = 12/51

Total probability = 1/4 * 12/51 =1 /17 or 0.0588