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Need explanation for probability problem.

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akpareek Senior | Next Rank: 100 Posts Default Avatar
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Need explanation for probability problem.

Post Wed Sep 04, 2013 9:03 am
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

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vishnum Junior | Next Rank: 30 Posts Default Avatar
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Post Thu Sep 05, 2013 9:35 pm
Hi Rich,

In the 10 ways of heads occurring 3 times we will have HTTHH etc.. But in the question we are interested only with HHHTT possibility only. Isn't it?

Br,
Vishnu.

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sanjoy18 Senior | Next Rank: 100 Posts Default Avatar
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Post Thu Sep 05, 2013 9:50 pm
Hi Vishnu,

"What is the probability that exactly 3 of the flips are heads?"
Above is the question that Rich posted..then question asked exactly 3 heads rather first three consecutive heads. hence the answer is 5/16

this problem can be solved by another method.actually it follows binomial probability
p(x)=probability of getting exactly x head in n trials
= ncx p^x (1-p)^(n-x)
here n=5 x=3
= 5c3 (1/2)^3 (1/2)^2
= 10*(1/8)*(1/4)
= 5/16

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vishnum Junior | Next Rank: 30 Posts Default Avatar
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Post Thu Sep 05, 2013 9:35 pm
Hi Rich,

In the 10 ways of heads occurring 3 times we will have HTTHH etc.. But in the question we are interested only with HHHTT possibility only. Isn't it?

Br,
Vishnu.

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sanjoy18 Senior | Next Rank: 100 Posts Default Avatar
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Post Thu Sep 05, 2013 9:50 pm
Hi Vishnu,

"What is the probability that exactly 3 of the flips are heads?"
Above is the question that Rich posted..then question asked exactly 3 heads rather first three consecutive heads. hence the answer is 5/16

this problem can be solved by another method.actually it follows binomial probability
p(x)=probability of getting exactly x head in n trials
= ncx p^x (1-p)^(n-x)
here n=5 x=3
= 5c3 (1/2)^3 (1/2)^2
= 10*(1/8)*(1/4)
= 5/16

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Post Thu Sep 05, 2013 11:35 pm
Hi vishnum,

It's true of ALL GMAT questions, but in this case, you really need to pay attention to what the question is asking you to solve. My example asked for ANY 3 of the 5 tosses to be heads, not necessarily the first 3. The way that the question is worded will define HOW you have to do the math. In many cases, some of the wrong answers are answers to different questions, so taking the time to understand the question and organize your work is a MUST.

GMAT assassins aren't born, they're made,
Rich

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Post Thu Sep 05, 2013 12:42 pm
Hi vinay1983,

With 5 coin flips, here's how you figure out the probability of flipping exactly 3 heads.

First, we calculate the total number of possible outcomes. Since each coin has 2 outcomes, the total outcomes is 5^2 = 32 total possibilities.

Now, since it doesn't matter which 3 tosses are heads, we use the combination formula to calculate all the different ways to get 3 heads...

5c3 = 5!/(3!2!) = 10 ways to get 3 heads.

Final answer for this question = 10/32 = 5/16

GMAT assassins aren't born, they're made,
Rich

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Contact Rich at Rich.C@empowergmat.com

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vinay1983 Legendary Member
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Post Thu Sep 05, 2013 2:23 am
Rich.C@EMPOWERgmat.com wrote:
Hi akpareek,

Brent's explanation is spot-on, so I won't rehash it here. What I will point out is that for this type of complex situation (5 tosses), the question is way too simple. So, what is the source of this prompt?

A far more likely GMAT-style question would be "What is the probability that exactly 3 of the flips are heads?"

GMAT assassins aren't born, they're made,
Rich
Rich, then what can be the answer for your question?(Explain)

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