Six coins are tossed 6400 times. Using Poisson distribution, find… - Vidyadip

Question

Six coins are tossed 6400 times. Using Poisson distribution, find approximate probability of getting six heads x times and 2 times.

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Answer

Let the coins be unbiased i.e. the probability of getting a head $=$ the probability of getting a tail, for each coin.
$\therefore$ The probability of getting 6 heads with 6 coins
$\begin{aligned} & =\left(\frac{1}{2}\right)^6=\frac{1}{64}=p(\text { say }) \\ n p & =6400 \times \frac{1}{64}=100=m(\text { say })\end{aligned}$
Let $X=$ no. of tosses with heads
Then according to Poisson distribution,
$P(X=x)=e^{-m} \frac{m^x}{x!}=e^{-100} \frac{(100)^x}{x!}$
$\text{and}\quad P(X=2)=e^{-m} \frac{m^2}{2!}$
$=e^{-100} \frac{(100)^2}{2!}=5000~e^{-100}$

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