Six Coins Are Tossed Simultaneously. What Is The Probability Of Getting Three Heads?


Let p represents the probability of getting head in a toss of a coin.


p = \( \frac{1}{2} \)

q = 1 – p

\( \Rightarrow 1 – \frac{1}{2} \\\Rightarrow \frac{1}{2} \)

Let x denote the random variable representing the number of heads in 6 tosses of a coin.

Probability of getting r sixes in n tosses of a fair is given by,

\(P(x = r) = \;^{6}{C}_{r}(\frac{1}{2})^{r}(\frac{1}{2})^{6-r} \)

Probability of getting three heads :

\( P (x = 3) = \;^{6}{C}_{3}(\frac{1}{2})^{3}(\frac{1}{2})^{6-3}\\\Rightarrow 20 *\frac{1}{2^{6}} = \frac{5}{16} \)

Therefore, the probability of getting three heads is \(\frac{5}{16}.\)

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