Cards of Deck Probability

Question

A.One card is drawn from a standard 52 card deck. Find the probability that it is a 7 or a Jack if drawing is done with replacement.

 

B.Two cards are drawn from a standard 52 card deck. Find the probability that a nine is drawn first and a 10 is drawn second if drawing is done with replacement.

 

P.S. Both A and B are different problems

Answer 1

Hi Jorge,

 

In a standard deck, there are 52 cards of 4 suits and 13 ranks. The cards of each rank appear in each of the 4 suits.

 

a) There are 4 sevens in the deck, and 4 Jacks in the deck. These results are independent, so there are 8 cards that satisfy the conditions of this draw.

P(7 or J) = 8/52 = 2/13

 

b) Because you're drawing with replacement, both draws have the entire deck to draw from.

P(9) = 4/52 = 1/13

P(10) = 4/52 = 1/13

P(9, then 10) = P(9) * P(10) = 1/13 * 1/13 = 1/169