Mathematics

What is the probability of getting at least one head when tossing 2 coins?

MTManish Tiwari · 12 Asked 15d ago 280 views 1 answer

I know the sample space is HH, HT, TH, TT. I tried to find the probability directly but I got confused. My teacher said to use the complement method. How does that work?

1 Answer

ABAditi Banerjee ✓ Accepted · 15d ago ▲ 17

Complement method: P(at least one head) = 1 - P(no heads at all) = 1 - P(TT). Sample space: {HH, HT, TH, TT} — 4 equally likely outcomes. P(TT) = 1/4. P(at least one head) = 1 - 1/4 = 3/4. Direct method: favourable outcomes = {HH, HT, TH} = 3 outcomes. P = 3/4. Both give the same answer! The complement method is faster when "at least one" events are involved, because "at least one head" includes many sub-events (exactly one head OR exactly two heads). It is easier to find the probability of the complement (zero heads) and subtract from 1.

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