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Toss a (fair) coin twice and find the probability that heads occurs EXACTLY once.

Sample Space $S$: $S = \{ H, H, T, T\}$ and $A = \{H, T\}$

Thus $1/4 + 1/4 = 1/2$.

But is this correct? The book points out that

$S = \{HT, TH, HH, TT \}$ is the correct sample space. Explain?

  • 0
    The problem with your soultion is that it accounts only for the outcome of 1 experiment twice. You need to considrt the outcome of both (once, of course) – 2017-01-06

1 Answers 1

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Either you toss a coin twice or tossing two coins is same thing.

Case 1-

Both Heads - HH

Case 2-

One Head and One Tail or One Tail and One Head - HT, TH

Case 3-

Both Tails - TT

Sample space = {HH, HT, TH, TT}

Favourable cases = {HT, TH}

Probability = $\frac{2}{4} = \frac{1}{2}$