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Six friends live in the city of Monrovia. There are four natural attra

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Six friends live in the city of Monrovia. There are four natural attra  [#permalink]

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New post 26 May 2019, 13:27
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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 same attraction?

A) (1/6)^4
B) (1/6)^3
C) (1/4)^6
D) (1/4)^5
E) (1/4)
Director
Director
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V
Joined: 24 Oct 2016
Posts: 714
GMAT 1: 670 Q46 V36
GMAT 2: 690 Q47 V38
GMAT 3: 690 Q48 V37
GMAT 4: 710 Q49 V38 (Online)
Re: Six friends live in the city of Monrovia. There are four natural attra  [#permalink]

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New post 26 May 2019, 13:27
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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 same attraction?

A) (1/6)^4
B) (1/6)^3
C) (1/4)^6
D) (1/4)^5
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 same attraction’. We don’t have a specific attraction given to us. So the selected attraction could be any one of the given four.

P(A) = No of ways in which all six can vote for the same attraction/Total no. of ways in which they can vote.

What is the no. of ways in which all six vote for the same attraction? They could all vote for the waterfall or for the safari or for the lake or for the caves. All of them can vote for the same attraction in 4 ways.

What is the no. of ways in which the friends can vote? As we saw in question no. 1, total no of ways in which the 6 friends can vote = 4*4*4*4*4*4 = 4^6

Therefore, P(A) = 4/(4^6)=1/(4^5)
ANSWER: D
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Re: Six friends live in the city of Monrovia. There are four natural attra  [#permalink]

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New post 02 Jul 2020, 07:20
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Re: Six friends live in the city of Monrovia. There are four natural attra   [#permalink] 02 Jul 2020, 07:20

Six friends live in the city of Monrovia. There are four natural attra

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