Find the probability.
-Seven slips of paper marked with the numbers 1, 2, 3, 4, 5, 6, and 7 are placed in a box and mixed Well. Two are drawn. What are the odds in favor of the sum of the numbers on the two selected Slips is not 6?
A) 9 to 1
B)21 to 2
C)19 to 2
D)19 to 1

Question

Quizplus · Accepted Answer

To find the odds in favor of the sum not being 6, first determine the total number of ways to draw 2 slips from 7, which is $C(7,2) = \frac{7!}{2!(7-2)!} = 21$. Then, find the combinations that sum to 6: (1,5), (2,4), and (5,1), (4,2) - but since drawing order doesn't matter, we only count each unique pair once, leaving us with 2 unique pairs. Thus, there are 21 - 2 = 19 outcomes where the sum is not 6. The odds in favor are 19 successful outcomes to 2 unsuccessful ones, or 19 to 2.

Find the Probability. -Seven Slips of Paper Marked with the Numbers 1, 2