Binomial distribution calculation

Question

If n=10 and p=0.6

find P(x=6)

Answer 1

The formula for binomial distribution is:

P_x = (_nC_x)pⁿq^n-x

Where _nC_x = n!/(x!(n-x)!)

Given:

n=10

p=0.6

q= 1-p = 0.4

x=6

Solve for P(x=6)

P(x=6)=P₆ = (₁₀C₆)(0.6)¹⁰(0.4)^10-6

P(x=6) = (10!/(6!(10-6)!))(0.6)¹⁰(0.4)⁴

P(x=6) = (210)(0.6)¹⁰(0.4)⁴

P(x=6) ≈ 0.0325