dabaobao wrote:
Six friends live in the city of Monrovia. There are four natural attractions around Monrovia – a waterfall, a safari, a lake and some caves. The friends decide to take a vacation together at one of these attractions. To select the attraction, each one of them votes for one of the attractions. What is the probability that each one of them votes for the safari?
A) (1/6)^4
B) (1/4)^6
C) (1/24)
D) (1/6)
E) (1/4)
Veritas Prep Official Solution
Here, A, the event for which we want to find the probability is ‘all six friends vote for the safari’
P(A) = No of ways in which all six can vote for the safari/Total no. of ways in which they can vote.
What is the no. of ways in which all six vote for the safari? Only one way. They all vote for the safari!
What is the no. of ways in which the friends can vote? Say, the friends are A, B, C, D, E and F. A can vote in 4 ways. B can vote in 4 ways. C can vote in 4 ways and so on… Total no of ways in which the 6 friends can vote = 4*4*4*4*4*4 = 4^6 (Using our old friend, the basic counting principle). We discussed this concept in our post on Unfair Distributions.
Therefore, P(A) = (1/4)^6
ANSWER: B