gprep 3 ps

[abhasjha]

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

why cant i use = nCr * p^r * q^(n-r)???

[GMATGuruNY]

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

P(H on the 1st flip) = 1/2.
P(H on the 2nd flip) = 1/2.
P(H on the 3rd flip) = 1/2.
P(T on the 4th flip) = 1/2.
P(T on the 5th flip) = 1/2.
Since we want all of these events to happen, we multiply the fractions:
1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 1/32.

The correct answer is E.

[GMATGuruNY]

why cant i use = nCr * p^r * q^(n-r)???

This formula would be appropriate if the question stem asked the following:
If the coin is flipped 5 times, what is the probability that it will land heads up EXACTLY 3 TIMES?
Here, good outcomes would include the following:
HHHTT
HTHHT
HTTHH.

The GMAT Prep problem is more constrained.
It asks for the probability that the only the FIRST 3 FLIPS are heads, implying that there is only ONE good outcome:
HHHTT.
Thus, the formula above is not appropriate.

[GMATinsight]

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

why cant i use = nCr * p^r * q^(n-r)???

Given: Probability of Head in 1 flip = 1/2 i.e. Coin is Fair

Probability = Favorable Outcome/Total Outcomes

The favorable Outcomes = 1 [i.e. HHHTT]
Total Outcomes = 2^5 = 32

Probability = 1/32

Answer: Option E

[GMATinsight]

why cant i use = nCr * p^r * q^(n-r)???

You can't use 5C3 here because 5C3 randomly selects 3 placements of Heads out of 5 placements in 5 flips and doesn't ensure that the Heads are obtained on first three outcomes and on last two

[abhasjha]

Thank you mitch and bhoopendra for clearing my doubt as to why 5c3... will not work .

[Brent@GMATPrepNow]

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

P(HEADS on 1st AND HEADS on 2nd AND HEADS on 3rd AND TAILS on 4th AND TAILS on 5th) = P(HEADS on 1st) x P(HEADS on 2nd) x P(HEADS on 3rd) x P(TAILS on 4th) x P(TAILS on 5th)
= 1/2 x 1/2 x 1/2 x 1/2 x 1/2
= [spoiler]1/32 = E[/spoiler]

Cheers,
Brent

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Hi abhasjha,

On probability, permutation and combination questions, it's essential to note the details so that you can set up whatever "math" is necessary to get to the correct answer. GMAT questions are carefully written to give you exactly what you need to know to do the work, so make sure that you're taking the proper notes, drawing pictures, etc. to keep track of everything.

In this prompt, I would write down:

HHHTT

So that I can remember what my "goal" is when solving.

You're clearly smart enough to answer many of these questions. To prove to Top Business Schools that you belong, you also have to show that you're organized.

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