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

Question

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. a seven​​​​​​​​​​​​ _____4 7's out of 52 cards: 4/52 = 1/13

 

b. a six of clubs​​​​​​​​​​​​ 1 out of 52 cards: 1/52

 

c. a five or a queen​​​​​​​​​​​ 4 5's + 4 Q's out of 52 cards: 8/52 = 2/13

 

d. a black card​​​​​​​​​​​​. Half the cards (26) are black 26/52 = 1/2

 

e. a red card or a jack​​​​​. 26 cards are black + 2 jacks that are red 28/52 = 7/13

 

f. a club or an ace​​​​​​​​​​​. 13 cards are clubs + 3 aces that are not clubs 16/52 = 4/13

 

g. a diamond or a spade​​​​​​​​​​​. 13 diamonds + 13 spades 26/52 = 1/2

 

Answer 2

Dazzmine

In each case the probability will be the number of interesting outcomes divided by the total number of possible outcomes.

As there are 52 cards, the total number of possible outcomes will be 52.

There are 4 suits (club, diamond, heart, spades), each with 13 cards, and each suit has ace - 2 to 10 - jack - queen - king.

Clubs and spades are black cards (so 26 black cards) and hearts and diamonds are red (26 red cards).

So for (a). How many sevens. There are 4 (7 CLUBS, 7 DIAMONDS, 7 HEARTS, 7 SPADES) so the probability will be 4/52 = 1/13 (you should simplify the fraction if you can).

So (b) (c) (d) (h) are straightforward - just count how many interesting outcomes there are and divide by 52 (that's an exercise for you).

(e) is a little trickier. Red card or a jack. Well 26 red cards. And 2 jacks not included in these - Jack of spades and jack of clubs. So 26 + 2 = 28 interesting outcomes. Probability 28 / 52 = 7 / 13

(f) - use same idea as (e). Exercise for you.

Mike