Playing Cards Probability Question

Question

There are 52 cards in a deck. 26 are red, and 26 are black. The 52 cards make up four suits (hearts, diamonds, spades, clubs). There are 13 of each suit (ace-10, jack, queen, king). Essentially it is a fair deck of cards.

 

a) What is the probability of drawing a 5?

b) What is the probability of drawing a red 5?

c) What is the probability of drawing the jack of hearts and then the jack of diamonds?

d) What is the probability of drawing the 4 of spades or a club?

e) What is the probability of drawing a 3 or a spade?

f) What is the probability of drawing the 10 of clubs or a king, and then a spade?

g) What is the probability of drawing a 7 or a heart, and then a 10 of hearts or a queen?

Answer 1

d) ) What is the probability of drawing the 4 of spades or a club? 

These two separate probabilities are 1/52 and 13/52, and they're mutually exclusive so you just add them: 5/52

 

c) What is the probability of drawing the jack of hearts and then the jack of diamonds?

P(J of hearts) is 1/52.  Then 51 other cards would remain; P(J of diamonds) = 1/51. Multiply these to get answer.

 

e) What is the probability of drawing a 3 or a spade? There are 4 threes and 13 spades, but one of the spades is a 3.

To satisfy the 'event' described in this problem, there are 16 possible draws, out of the 52 cards; P(event 'e') = 16/52 which reduces to 4/13.

 

Answer 2

a) 4/52 =1/13

b) 2/52= 1/26