Question

Joe dealt 20 cards from a standard 52-card deck, and the number of red cards exceeded the number of black cards by 8. he reshuffled the cards and dealt 30 cards. this time, the number of red cards exceeded the number of black cards by 10. determine which deal is closer to the 50/50 ratio of red/black expected of fairly dealt hands from a fair deck and why.

a. the first series is closer because 1/10 is farther from 1/2 than is 1/8.
b. the series closer to the theoretical 50/50 cannot be determined unless the number of red and black cards for each deal is given.
c. the second series is closer because 20/30 is closer to 1/2 than is 14/20.
d. the first series is closer because the difference between red and black is smaller than the difference in the second series.

Answer 1

first deal there are 14 red and 6 black so fraction of red = 14/20 or 0.7
second deal there are 20 red and 10 black so fraction of red = 20/30 or 0.67

0.67 is closer to 1/2 that 0.7 so

c is the correct choice

Answer 2

d)

Explanation:

In the first shuffle, Joe gets 6 black cards and 14 red cards (6:14⇒3:7)

In the second shuffle, Joe gets 10 black cards and 20 red cards (10:20⇒1:2)

The first series is closer to the 50:50 radio because 3:7 is closer to 50:50 given that the difference between read and black is smaller than the difference in the second series.