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Failure is Often Easier than Success

If five coins are flipped simultaneously, what is the probability that at least two will be heads?

Answer = 13/16

Explanation: If at least two need to be heads than the opposite of that would be zero heads or one head. Since each event has two possible outcomes and there are five events, there will be a total of 32 (25) events. There is only one possible event for zero heads (TTTTT). There are five different events for one head (HTTTT, THTTT, TTHTT, TTTHT, TTTTH). This gives us a total of 6 "unfavorable" events. The probability of failure is equal to 6/32 or 3/16. Now we simply use our formula of Probability of Success = 1 - Probability of Failure which yields our answer of 13/16. Go ahead and try to do it the hard way. We dare you!

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