six coins

nidhis.1408 wrote:If six coins are flipped simultaneously, the probability of getting at least one pair is closest to:

a. 3%
b. 6%
c. 75%
d. 94%
e. 97%

Hi nidhis.1408!

I'm going to assume that you mean "the probability of getting at least one HEAD" ", because otherwise the probability is CERTAIN (100%) that if you flip 6 coins, at least 2 of them will have the same thing showing (a pair of heads or a pair of tails).

So if I want to solve directly for the probability of AT LEAST ONE head, I will have to find the probability of 1 head, 2 heads, 3 heads, 4 heads, 5 heads, and 6 heads, and then add them up!! But that is a TON of work. Why not look for the probability of the one option I DON'T want (the probability of NO heads) and then subtract that from 0.

The probability of NO heads = pr(TTTTTT) so (1/2)(1/2)(1/2)(1/2)(1/2)(1/2) = 1/64.

That means the probability of anything BUT that happening would be 1 - (1/64) = 63/64.

Do the long division and we can quickly see that this probability is over 98% (which is not a choice so this isn't terribly accurate by GMAT standards), but the closest answer would be E.

Hope this helps!

Whit

nidhis.1408 wrote:The question actually says- the probability of getting at least 1 PAIR.

One pair? As in "at least 2 heads, or at least 2 tails"?
If so, then the probability is 1.
There will always be at least 2 heads, or at least 2 tails.

Cheers.
Brent

Or perhaps 6 dice are rolled (as opposed to 6 coins tossed)??

Cheers,
Brent

nidhis.1408 wrote:The question actually says- the probability of getting atleast 1 PAIR.

Hi nidhis.1408!

If the problem was correctly transcribed as:
If six coins are flipped simultaneously, the probability of getting at least one pair is closest to...

Then I would be very skeptical of the source for a couple of reasons:
(1) pairs of what? the GMAT would be explicit here and either do a better job of describing what 1 pair means OR would likely give you a couple of examples HHTTTT has 1 pair of heads and 2 pairs of tails.

(2) the answers are not correct! as Brent and I both mention in our posts - the probability of flipping 6 coins and having at least 2 heads or 2 tails in the bunch is perfect certainty or 100% (and the GMAT would never approximate this as 97% or anything other than 100%).

So always be careful where you find your practice material. Bad advice is far worse than no advice - and studying from bad sources is basically begging for bad advice!!

Hope this helps!

Whit