Question

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

Answer 1

we know,
Probability of getting one head with one coin = 1/2 [ n(E) = 1 , n(S) = 2 {∵ H , T } so, P(E) = 1/2]
∴ probability of getting six heads with six coins, P(E) = (1/2)⁶ = 1/2⁶ = 1/64
If six coins are tossed 6400 times , then nP(E) = 6400 × 1/64 = 100 = m [ Let ]
According to poisson's distribution ,
P(x = r) = $\bold{\frac{e^{-m}m^r}{r!}}$
Here, probability of getting six heads in r times ,
so, r = 2 , m = 100
Hence, P(x = 2) = $\bold{\frac{e^{-100}100^2}{2!}}=\bold{e^{-100}5000}$