Question

QUESTION 16

A company that produces Headphones has two different plant locations, one located in North Carolina and one in Montana. In North Carolina there are 80 employees and in Montana there are 55 employees. The company wants to test their newest headphones and has decided to give away 30 pairs to a randomly selected group of employees. Compute the following probabilities.

What is the probability that half the headphones go to employees at the Montana plant?

QUESTION 17

What is the probability that at least 10 employees at the Montana plant receive headphones?

QUESTION 18

What is the probability that 15 or fewer employees at the North Carolina plant receive headphones?

QUESTION 19

What is the probability that fewer than 19 employees at the North Carolina plant receive headphones?

QUESTION 20

What is the probability that more than 15 employees at the Montana plant receive headphones?

 

Answer 1

We have 30 earphones to distribute among 80 employees of NC and 55 employees of M.

The total number of ways to distribute 30 earphones to 135 employees =

16)

Probability that half the headphones go to employees at the Montana plant:

That means 15 go to M and 15 go to NC.

The no. of ways of 15 earphones going to M =

The no. of ways of 15 earphones going to NC =

Hence, the prob. that half the earphones go to M =

17)

Probability that at least 10 employees at the Montana plant receive headphones:

The total number of ways : (10 of M x 20 of NC) + (11 of M x 19 of NC) + (12 of M x 18 of NC) + .... + (30 of M x 0 of NC)

A shorter way would be to find :

(0 of M x 30 of NC) x (1 of M x 29 of NC) + .... + (9 of M x 21 of NC) /

and then subtract the above from 1 to find the required probability.

18) The probability that 15 or fewer employees at the North Carolina plant receive headphones:

Required number of ways : ( 30 of M x 0 of NC) + (29 of M x 1 of NC) + (28 of M x 2 of NC) + .... + (15 of M x 15 of NC)

Required prob. = Required number of ways /    

19)

The probability that fewer than 19 employees at the North Carolina plant receive headphones:

Required number of ways : ( 30 of M x 0 of NC) + (29 of M x 1 of NC) + (28 of M x 2 of NC) + .... + (12 of M x 18 of NC)

Required prob. = Required number of ways /    

20)

The probability that more than 15 employees at the Montana plant receive headphones:

Required number of ways : ( 15 of M x 15 of NC) + (16 of M x 14 of NC) + (17 of M x 13 of NC) + .... + (30 of M x 0 of NC)

Required prob. = Required number of ways /