can you help me solve this

Question

Assume Binomial Distribution with n = 10 and p = 0.6. Please show your answers to 4 decimal places.

P(X == 4) =  

P(X ≤≤ 4) =   

P(X << 4) =   

P(X >> 4) =   

P(X ≥≥ 4) = 

Answer 1

Recall that for variable X which follows Binomial (n,p), the probability:

$P(X=x) = ${n \choose x} \times p^{x} \times (1-p)^{n-x}$

Therefore,

$P(X=4) =\{10 \choose 4 \} \times 0.6^{4} \times (1-0.6)^6 = 0.1114$,

$P(X \leq 4) = P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4) = 0.1662$