# Algebra

Three quarters are tossed and a tail appears on at least one of them. What is the probability that at least one head appears? Express as a common fraction.

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1. 2/3, because there are 3 coin flips, but one is already tails, so there's only 2 more chances to get heads.

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2. Well basically, just count how many total combinations there are in the flips.

= HHH, HHT, HTH, THH, TTH, THT, HTT, TTT

Of those, we find 7 with a tail (we omit HHH from our list).
Now with that, we count the ones with at least one head.

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3. There are a total of eight possible outcomes for three coins: HHH, HHT, HTH, THH, TTH, THT, HTT, and TTT. Of these eight outcomes, seven of them show at least one tail (all except HHH).

Counting, we find six of these seven outcomes have at least one head, so the probability is 6/7.

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