What is the probability that all 6 coins tossed together will turn up

How about an easier way?!?!

How many total possible outcomes are there if we toss six coins? 2*2*2*2*2*2 = 2^6 = 64
But are all of those allowable? No, we need to eliminate any that don't have at least two heads.
How many ways are there to get 0 heads? 1
How many ways are there to get 1 heads? 6
Okay, so that's 7 configurations that aren't possible because we know we have to have at least two heads.
That leaves us with 64-7 = 57 allowable configurations.
How many of them "win?" Just one: HHHHHH.
So, the probability is 1/57.

Answer choice D.


For those who are curious, let's address why 1/2^4 doesn't work.
That would be the answer if we knew that two SPECIFIC coins landed heads. Imagine I say that first two coins land heads and ask what's probability that the remaining four also land heads. We'd have H H _ _ _ _. Now your 1/2^4 would work. But we just know that SOME two coins landed heads.


ThatDudeKnowsProbability