Use counting rules to determine the probability.
-A committee of 11 members is voting on a proposal. Each member casts a yea or nay vote. On a random voting basis, what is the probability that the proposal wins by a vote of 8 to 3?
A)0.16113
B)0.08057
C)0.03833
D)0.04028

Question

Use counting rules to determine the probability.
-A committee of 11 members is voting on a proposal. Each member casts a yea or nay vote. On a random voting basis, what is the probability that the proposal wins by a vote of 8 to 3? 
A)0.16113
B)0.08057
C)0.03833
D)0.04028

Quizplus · Accepted Answer

The probability is calculated by finding the number of favorable outcomes (8 yea votes) divided by the total possible outcomes. The number of ways to choose 8 yea votes out of 11 is given by the combination formula C(11,8). The total number of voting outcomes is 2^11. Thus, the probability is C(11,8)/2^11 = 165/2048 = 0.08057.

Use Counting Rules to Determine the Probability