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.
HELP!!!!
2x + 8 = 20
2x = 12
x = 6
red/black = 14/6
Repeat for second deal.
I came up with choice A. Is that right?
Are you really looking for the "ratio of red/black"?
Since the red cards are greater than the black cards, you have a ratio of red to black > 1. If it is black to read, then 6/14 = 3/7
I would disagree.
To determine which deal is closer to the 50/50 ratio of red/black, we need to compare the differences between the number of red cards and black cards in each deal.
In the first deal, the number of red cards exceeded the number of black cards by 8. This means that if we let R represent the number of red cards and B represent the number of black cards, we have the equation R - B = 8.
In the second deal, the number of red cards exceeded the number of black cards by 10. Again using R and B to represent the number of red and black cards respectively, we have the equation R - B = 10.
Now, let's compare the differences in both deals:
For the first deal, the difference in red and black cards is 8 (R - B = 8).
For the second deal, the difference in red and black cards is 10 (R - B = 10).
To determine which difference is closer to the 50/50 ratio, we can compare the absolute values of the differences. The absolute value of a number is its distance from zero.
In the first deal, the absolute value of the difference is |8| = 8.
In the second deal, the absolute value of the difference is |10| = 10.
From the comparison, we can see that the first deal has a smaller absolute value of the difference, which means the difference between the number of red and black cards is smaller. Hence, the first deal is closer to the 50/50 ratio of red/black.
Therefore, the correct answer is D. The first series is closer because the difference between red and black is smaller than the difference in the second series.