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24 votes

Suppose three coins are lying on a table, two of them with heads facing up and one with tails facing up. One coin is chosen at random and flipped. What is the probability that after the flip the majority of the coins(i.e., at least two of them) will have heads facing up?

  1. $\left(\frac{1}{3}\right)$
  2. $\left(\frac{1}{8}\right)$
  3. $\left(\frac{1}{4}\right)$
  4. $\left(\frac{1}{4}+\frac{1}{8}\right)$
  5. $\left(\frac{2}{3}\right)$
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6 Answers

Best answer
28 votes
28 votes

(e) is correct

Table has $3$ coins with $H,H,T$ facing up.

Now, probability of choosing any coin is $\dfrac{1}{3}$ , as we can chose any of the three coins.

Case A: $1^{st}$ coin :  either $H$ or $T$ can come.
                    so, $HHT ,THT$ possible.only $HHT$ is favorable.
                    which gives $\left(\dfrac{1}{3}\right)\times \left(\dfrac{1}{2}\right)= \dfrac{1}{6}.$

Case B: $2nd$ coin :  either $H$ or $T$ can come.
                    so, $HHT, HTT$ possible.only $HHT$ is favourable.
                    which gives $\left(\dfrac{1}{3}\right)\times \left(\dfrac{1}{2}\right)=\dfrac {1}{6}.$

Case C:  $3rd$ coin : Table already contains two $H's$ so, whatever comes is favourable.
                    which gives $\left(\dfrac{1}{3}\right)\times 1 =\dfrac {1}{3}.$

Summing up the total gives $\dfrac{1}{6} +\dfrac {1}{6} +\dfrac {1}{3} =\dfrac {2}{3}.$

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6 votes
6 votes

We have coin lying on table.

we have to select one coin ad then toss it.

In starting we have  {H,H,T }  outcome

Now from here we can only select one coin then flip it.

So,number of all posible outcomes are those which have 1 or 0 hamming distance from above outcome.

Here total outcomes are ---6

And  outcomes with at least two heads are----4

Ans is=4/6=2/3

1 votes
1 votes
For selecting a head faces coin probability is $2/3$

After selecting one head facing coin the probability that it changes to a tail after the toss is $1/2$

So the probability for not getting majority of the coins not facing head is $((2/3)*(1/2))=1/3$

From this the majority of the coins facing head is $ =1-(1/3)$

                                                                                $ =2/3$
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