Probability

Question

Hello! I have a question about probability that I got for homework that I can't figure out. It would help if you told me how to solve this and future problems with the key words "and then" as in like roll a 4 on a die and then a 1. Thanks you very much!

 

'What is the probability of drawing a 7 and then an 8 in a deck of 52 playing cards?'

'What is the probability of drawing a red seven and then a black eight?'

Answer 1

There are 4 7's in the deck of 52 so the p(7)=4/52 and since drawing a seven and an 8 are independent events the p(7 and then 8)= p(7)*p(8/7) =(4/52)*(4/51) =.005919. Not very likely.

 

Jim

Answer 2

52 cards in a deck, 4 of which are 7s

 

Probability of drawing a seven is 4/52

 

After drawing a 7, there are 51 cards left, 4 of which are 8s.

 

Probability of drawing an 8 is 4/51

 

Probability of drawing a 7 then an 8 = 4/52*4/51

 

It works the same for "red 7s" and black 8s", except there are only 2 of each in the deck instead of 4.