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# A group of friends have decided to take a roadtrip. Whenever

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01 Oct 2005, 21:39
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A group of friends have decided to take a roadtrip. Whenever they come to a fork in the road, they will flip a fair coin to decide whether to head right or left. If the coin is heads, they will head right. If the coin is tails, they will head left. If the friends have made seven decisions, what is the probability that they took exactly four lefts?

A. 1/16
B. 1/32
C. 21/25
D. 35/128
E. 4/7
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02 Oct 2005, 00:21
d) 35/128

7C4*(1/2)^4*(1/2)^3 = 35/(16*8)=35/128
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02 Oct 2005, 04:18
D too
I used bernoulli method too as chets did
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02 Oct 2005, 04:27
OA is D.

Antmavel, could you please explain the bernoulli method??
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02 Oct 2005, 06:08
D) Same method ... applying the formula nCr*(p^r)*(q^(n-r))

When to apply Bernoulli's trials....
1) Only two possible outcomes for each trial (Yes or No, Heads or Tail, or simply p=Success & q= Failure. Note: p need not be same as q)
2) The probability of success (p) is same for each trial
3) Trials are independent (n is independent)

So in this problem, there are seven trials and you want to find the probability of success for exactly 4 of them.
For 1 trial Success is: p= 1/2 (its either Yes or No)
q = 1-p = 1/2
n =7
r=4
Applying BT, you get 35/128.

Added: I also found the following link on this website (see Appendix A) http://www.gmatclub.com/content/courses/quantitative/probability.php
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-Vikram

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02 Oct 2005, 20:36
GMATT73 wrote:
OA is D.

Antmavel, could you please explain the bernoulli method??

vikramm, your post was perfect Nice explanation
02 Oct 2005, 20:36
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# A group of friends have decided to take a roadtrip. Whenever

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