Sample Space = {HH, TH, HT}

Favorable case ={HH}

=1/3

Favorable case ={HH}

=1/3

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If two fair coins are flipped and at least one of the outcomes is known to be a head, what is the probability that both outcomes are heads?

- $\left(\dfrac{1}{3}\right)$
- $\left(\dfrac{1}{4}\right)$
- $\left(\dfrac{1}{2}\right)$
- $\left(\dfrac{2}{3}\right)$

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Best answer

21 votes

When two coins are flipped , sample space is { HH, HT, TH, TT }

Now if it is known that at least one of them is head then, reduced sample space will be --> { HH, HT, TH}

In this reduced sample space only one sample point fulfilling the criteria( both are heads HH) hence required probability is 1/3

Now if it is known that at least one of them is head then, reduced sample space will be --> { HH, HT, TH}

In this reduced sample space only one sample point fulfilling the criteria( both are heads HH) hence required probability is 1/3