Three coins are tossed once. Find the probability of getting (i) $3$ heads (ii) $2$ heads

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Three coins are tossed once. Find the probability of getting (i) $3$ heads (ii) $2$ heads

When a coin is tossed the possible outcomes are either a Head $\left( H \right)$ or Tail $\left( T \right)$ .

Here, coin is tossed three times then the sample space contains,

$S{\text{ }} = {\text{ }}\left\{ {HHH,{\text{ }}HHT,{\text{ }}HTH,{\text{ }}THH,{\text{ }}TTH,{\text{ }}HTT,{\text{ }}TTT,{\text{ }}THT} \right\}$

And $n\left( S \right){\text{ }} = {\text{ }}8$ .

(i) $3$ heads

Suppose $A$ be the event of getting $3$ heads

Then, $n\left( A \right) = {\text{ }}1$

$P(A) = \frac{{n(A)}}{{n(S)}}$

Therefore, $P(A) = \frac{1}{8}$ .

(ii) $2$ heads

Suppose $B$ be the event of getting $2$ heads

Then, $n{\text{ }}\left( A \right){\text{ }} = {\text{ }}3$

$P(B) = \frac{{n(B)}}{{n(S)}}$

Therefore, $P(B) = \frac{3}{8}$ .

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