akpareek wrote: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

We want 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

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

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

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