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%
a. 3%
b. 6%
c. 75%
d. 94%
e. 97%
Hi nidhis.1408!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%
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
