Question

Please show work.

What are the probabilities that, from a normal pack of playing cards:

A. A single card picked blind will be a diamond?

B. A deuce of hearts will be removed followed by a diamond?

C. A single card picked will be either a diamond or a spade?

D. Four cards picked out will be two aces and two queens?

(Assume that, in parts B and D, each card that is removed from the deck is replaced and the deck shuffled before the next card is removed.)

Answer 1

Some knowledge of cards before we solve the probabilities:

There are 52 cards in a pack and there are 4 different suits i.e hearts, diamond , spades and clubs.
13 cards of each suits.(Ace to 10 and one joker , queen and king.)

a)A single card picked blind will be a diamond?

Since there are 13 cards of diamonds in 52 cards therefore the probability of selecting a diamond from 52 cards is:

b)A deuce of hearts will be removed followed by a diamond

Since there is only one deuce of heart therefore probability of selecting it is :1/52

and probability of selecting a diamond is:13/52( since we are replacing the cards)

Therefore the collective probability is :

c)A single card picked will be either a diamond or a spade?

Since there are 13 of each diamond or spade therefore the collective probability is :

d) Four cards picked out will be two aces and two queens?

Since there are 4 aces and 4 queens therefore picking one by one the collective probability is :