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+14 votes

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?

  1. $\left(\dfrac{1}{3}\right)$
  2. $\left(\dfrac{1}{4}\right)$
  3. $\left(\dfrac{1}{2}\right)$
  4. $\left(\dfrac{2}{3}\right)$
asked in Probability by Veteran (96.1k points)
edited by | 2.1k views
Sample Space = {HH, TH, HT}
Favorable case ={HH}

3 Answers

+20 votes
Best answer

Answer - A

prob(at least one head) = $\dfrac{3}{4}$

prob(both heads) =$\dfrac{1}{4}$

using bayes' theorem =$\dfrac{\left(\dfrac{1}{4}\right)}{\left(\dfrac{3}{4}\right)} =\dfrac{1}{3}.$

answered by Loyal (8.7k points)
edited by
I did small mistake, I took it first case is head ad then what is the outcome!

In this case, answer can be 1/4 na??
^^if 1st is head then it will be 1/2
+10 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
answered by Active (2.4k points)
+2 votes
Using conditional probabilty

P(A/B) = P(A∩B)/P(B)




P(A∩B) =  1/4

P(B) = 3/4

 the probability is 1/4/(3/4)=1/3
answered by Active (3.9k points)

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