Question

Six coins are tossed 6400 times. using poisson distribution what is the approximate probability of getting six heads ‘r' times

Answer 1

the answer is :
(1/2)^6*r times
=1/64*r times

Answer 2

Answer:

The approximate probability of getting six heads ‘r' times is

$P(X=r)=\frac{100^re^{-100}}{r!}$  

Step-by-step explanation:

Given : Six coins are tossed 6400 times.

To find : What is the approximate probability of getting six heads ‘r' times?

Solution :

Coin has two faces one tail and one head.

Probability of getting one head is $\frac{1}{2}$

Probability of getting six heads with six coins is $(\frac{1}{2})^6=\frac{1}{64}$

Now, The average number of six coins are tossed 6400 times getting 6 heads is $6400\times \frac{1}{64}=100$

So, The mean of the Poisson distribution is $\lambda=100$.

The Poisson distribution formula is given by,

$P(X=x)=\frac{\lambda^xe^{-\lambda}}{x!}$

Substituting the values,

$P(X=r)=\frac{100^re^{-100}}{r!}$

Therefore, The approximate probability of getting six heads ‘r' times is

$P(X=r)=\frac{100^re^{-100}}{r!}$