Coin Flip Strategy

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priyankamishra11: Master | Next Rank: 500 Posts; Posts: 120; Joined: Thu May 15, 2008 1:07 pm; Location: Boston .US; Thanked: 1 times

Coin Flip Strategy

by priyankamishra11 » Sat Sep 27, 2008 4:08 pm

Hi ,

I wanted to apply coin flip strategy given by Stuart " www.beatthegmat.com/coin-flip-questions ... 17911.html " in the following question, but I am not getting the answer can someone please explain what is wrong?

If a certain coin is flipped, the probability that the coin will land heads is 1/2. If the coin is flipped 5 times, what is the probability that it will land heads up on the first 3 flips and not on the last 2 flips?

A. 3/5
B. 1/2
C. 1/5
D. 1/8
E. 1/32

Regards,
Priyanka

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Source: Beat The GMAT — Problem Solving | Sat Sep 27, 2008 4:08 pm

cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pm; Thanked: 331 times; Followed by:11 members

by cramya » Sat Sep 27, 2008 4:19 pm

I am also eager to know how to apply the pascal triangle coin flip strategy here.

I just did

p(hhhtt) = 1/2*1/2*1/2*1/2*1/2 = 1/32

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priyankamishra11: Master | Next Rank: 500 Posts; Posts: 120; Joined: Thu May 15, 2008 1:07 pm; Location: Boston .US; Thanked: 1 times

by priyankamishra11 » Sat Sep 27, 2008 4:33 pm

yes thats how I did it, but I am not getting this same answer by applying either coin flip formula or pascal triangle.

Can someone explain it?

Regards,
Priyanka

Quote

stop@800: Legendary Member; Posts: 871; Joined: Wed Aug 13, 2008 7:48 am; Thanked: 48 times

by stop@800 » Sun Sep 28, 2008 6:30 am

Total possible outcomes = 2^5 = 32
Favorable is just one ie HHHTT
so
Ans IMO is 1/32

www.interrogationpoint.com

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stop@800: Legendary Member; Posts: 871; Joined: Wed Aug 13, 2008 7:48 am; Thanked: 48 times

by stop@800 » Sun Sep 28, 2008 6:37 am

You need 3 heads out of 3 and
2 tails out of 2

We need to carefully apply pascal triangle.

We need 3 heads out of first 3 toss so apply pascal of 3 coins
and 2 tails from last 2 tails so apply pascal of 2 coins
and multiple those

from 1331
we will get 1 favorable and total 8

for two coins it is
121
hence 1 / 4

so 1/4 * 1/8

= 1 / 32

Hope this helps!!

www.interrogationpoint.com

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pm; Location: Toronto; Thanked: 1710 times; Followed by:614 members; GMAT Score:800

Re: Coin Flip Strategy

by Stuart@KaplanGMAT » Sun Sep 28, 2008 7:59 pm

priyankamishra11 wrote:Hi ,

I wanted to apply coin flip strategy given by Stuart " www.beatthegmat.com/coin-flip-questions ... 17911.html " in the following question, but I am not getting the answer can someone please explain what is wrong?

If a certain coin is flipped, the probability that the coin will land heads is 1/2. If the coin is flipped 5 times, what is the probability that it will land heads up on the first 3 flips and not on the last 2 flips?

A. 3/5
B. 1/2
C. 1/5
D. 1/8
E. 1/32

This isn't a great question for the Triangle - there's a much easier way to solve.

We know that probability = #desired/total#

In this case, we have only 1 desired outcome: HHHTT

We know that for 5 flips, there are 2^5 = 32 total possible outcomes.

So, the answer is simply 1/32.

I suppsed you could make things far more complicated as stop@800 did and apply the Triangle that way (his solution is perfect), but that seems like a lot of extra effort!