1. ## binomial

sorry, im really dumb.. but here's the question

A person researching business-to-business communications found 90% of people used email as their primary means of communication. If there were 20 B2B operators contacted for a future research study focused solely on email communication, what is the probability that none of the 20 will use email in B2B as their primary form of communication?

(a) $0.1^{20}$
(b) $1 - 0.1^{20}$
c) $0.9^{20}$
d) $1 - 0.9^{20}$

i know the answer is a

but can someone just explain to me, why didnt they sub the values in the binomial formula? coz i thought that you have to use the full formula when calculating the binomial, but then why did they only use a part of it?

2. Originally Posted by gconfused
sorry, im really dumb.. but here's the question

A person researching business-to-business communications found 90% of people used email as their primary means of communication. If there were 20 B2B operators contacted for a future research study focused solely on email communication, what is the probability that none of the 20 will use email in B2B as their primary form of communication?

(a) $0.1^{20}$
(b) $1 - 0.1^{20}$
c) $0.9^{20}$
d) $1 - 0.9^{20}$

i know the answer is a

but can someone just explain to me, why didnt they sub the values in the binomial formula? coz i thought that you have to use the full formula when calculating the binomial, but then why did they only use a part of it?
It helps to define the random variable and hence get things clear in your head:

Let X be the random variable number of people that will use email in B2B as their primary form of communication.

X ~ Binomial(n = 20, p = 0.9)

$\Pr(X = 0) = {20 \choose 0} (0.9)^0 (1 - 0.9)^{20 - 0} = 1 \times 1 \times 0.1^{20}$.