Binomial Distribution — Maths STD 12 Science — Question
Gujarat BoardEnglish MediumSTD 12 ScienceMathsBinomial Distribution2 Marks
Question
Six coins are tossed simultaneously. Find the probability of getting. 3 heads.
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Answer
Let p represents the probability of getting head in a toss of fair coin, so $\text{p}=\frac{1}{2}$ $\text{q}=1-\frac{1}{2}$ [Since p + q = 1] $\text{q}=\frac{1}{2}$ Let X denote the random variable representing the number heads in 6 tosses of coin. probability of getting r sixes in n tosses of a fair coin is given by, $\text{P(X = r})=\text{ }^\text{n}\text{c}_{\text{r}}\text{p}^{\text{r}}\text{q}^{\text{n}-\text{r}}$3 $=\text{ }^6\text{c}_{\text{r}}\big(\frac{1}{2}\big)^{\text{r}}\big(\frac{1}{2}\big)^{6-\text{r}}\dots(1)$ Probability of getting 3 heads $=\text{P(X}=3)$ $=\text{ }^6\text{c}_3\big(\frac{1}{2}\big)^3\big(\frac{1}{2}\big)^{6-3}$ $=\frac{6\times5\times4}{3\times2}\big(\frac{1}{2}\big)^3\big(\frac{1}{2}\big)^3$ $=\frac{20}{64}$ Probability of getting 3 heads $=\frac{20}{64}=\frac{5}{16}$
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