Latest self Aptitude Question SOLUTION: If six coins are flipped simultaneously, the probability of getting at least one pair is closest to:

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(#M40012485) SELF question Keep an EYE

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

sathyapriya (11 years ago)

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sathyapriya  (11 years ago)

WIth "at least" probability in a sequence of events, it's often easier to find the probability of "none" and subtract from 100%. Here, there are many ways to get at least one pair, including: Heads-Tails-Heads-Tails-Heads-Heads; Tails-Tails-Tails-Tails-Tails-Heads, etc. But only two sequences will not arrive at at least one pair: all heads, or all tails. So 2 of the potential outcomes do not work. And there are 6 individual decision points, each with two options, so there are 2 * 2 * 2 * 2 * 2 * 2 = 64 total outcomes. 2 of the 64 do not work, and that reduces to 1/32. 1/33 would be 3.33%, so 1/32 is a bit greater than that (approximately 3.5%). The remaining approximately-96.5% of outcomes do produce at least one pair, so the correct answer is 97

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