Question

What’s the probability of getting each card out of a deck?

Determine the probability of drawing the card(s) at random from a well-shuffled regular deck of 52 playing cards.​
​
a. a seven​​​​​​​​​​​​ __________

b. a six of clubs​​​​​​​​​​​​. ___________

c. a five or a queen​​​​​​​​​​​ ___________

d. a black card​​​​​​​​​​​​. ___________

e. a red card or a jack​​​​​. ___________

f. a club or an ace​​​​​​​​​​​. ___________

g. a diamond or a spade​​​​​​​​​​​. ___________

Answer 1

a. 1/13

b. 1/52

c. 2/13

d. 1/2

e. 15/26

f. 17/52

g. 1/2

Explanation:

a. In a deck of cards, there are 4 suits and each of them has a 7. Therefore, the probability of drawing a 7 is:

P(7) = 4/52 = 1/13

b. There is only one 6 of clubs, therefore, the probability of drawing a 6 of clubs is:

P(6 of clubs) = 1/52

c. There 4 fives (one for each suit) and 4 queens in a deck of cards. Therefore, the probability of drawing a five or a queen​​​​​​​​​​​ is:

P(5 or Q) = P(5) + P(Q)

= 4/52 + 4/52

= 1/13 + 1/13

P(5 or Q) = 2/13

d. There are 2 suits that are black. Each suit has 13 cards. Therefore, there are 26 black cards. The probability of drawing a black card is:

P(B) = 26/52 = 1/2

e. There are 2 suits that are red. Each suit has 13 cards. Therefore, there are 26 red cards. There are 4 jacks. Therefore:

P(R or J) = P(R) + P(J)

= 26/52 + 4/52

= 30/52

P(R or J) = 15/26

f. There are 13 cards in clubs suit and there are 4 aces, therefore:

P(C or A) = P(C) + P(A)

= 13/52 + 4/52

P(C or A) = 17/52

g. There are 13 cards in the diamonds suit and there are 13 in the spades suit, therefore:

P(D or S) = P(D) + P(S)

= 13/52 + 13/52

= 26/52

P(D or S) = 1/2