Question

Calculate the following binomial probability by either using one of the binomial probability tables, software, or a calculator using the formula below. Round your answer to 3 decimal places.

P(x | n, p) =

n!

(n − x)! x!

· p^x · q^{n − x}    where    q = 1 − p

P(x ≥ 2, n = 6, p = 0.4) =

Answer 1

I provided both methods

1. Using formula ( pictures are attached)

2. Using Software R.(code is given below)

R Code :-

#Calculating Binomial probability

n <- 6 # defining parameter n
p <- 0.4 #defining probability of success

a <- dbinom(x= 2:6,size = n, prob = p)#here vector "a" contains probability of every random variable greater than and equal to 2

sum(a)#here we are summing all the probability associated with random variables which are greater than and equal to 2 so now we have probability of x>=2.