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

Sol:

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

So

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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