Question

# 1.) The binomial formula has two parts. The first part of the binomial formula calculates the...

1.) The binomial formula has two parts. The first part of the binomial formula calculates the number of combinations of X successes. The second part of the binomial formula calculates the probability associated with the combination of success and failures. If N=6 and X=5, what is the number of combinations of X successes?

2.)

I play a light game with my daughter. We have a small hand-held projector that displays an image on the ceiling from a small interchangeable plastic insert. You cannot tell the image on the insert until you project it on the ceiling. There are three inserts with three unique pictures: Elsa, Anna, and Olaf. We randomly pick one and guess before projecting the answer. Each time we replace the insert and repeat the experiment three times.

How many different combinations of correct and incorrect are there in the sample space for this experiment?

1.

Given,

n = 6

x = 5

Let us consider,

Binomial distribution P(X = x) = nCx*p^x*q^(n-x)

Here it has the 2 parts,

i.e.,

(i)

Number of combinations of X successes.

(ii)

The probability associated with the combination of success and failures

Here we need only number of combinations of X successes.

nCr = n!/(n-r)!*r!

6C5 = 6!/(6-5)!*5!

= 6

Hence number of combinations of X successes = 6

Please post the remaining the remaining question as separate post. Thank you.