Question

On the occasion of the annual day function, it has been decided that all the employees will dress either red or black. Consider there are n employees.
(A) What is the probability that all employees will dress black?
(B) What is the probability that all employees will dress red?
(C) Explain why the sum of possibilities of (a) and (b) isn't equal to 1.

The board of directors of Tarbell Industries consists of eight men and four women. A four-member search committee is to be chosen at random to conduct a nationwide search for a new company president.
(a) What is the probability all four members of the search committee will be women?
(b) What is the probability all four members will be men?

Answer 1

1. A) Probability that all employees will dress black = (1/2)^n

Since Probability of each dressing black = 1/2

B) Probability that all employees will dress red = (1/2)^n

Since Probability of each dressing red = 1/2

C) Sum of probability of a and b is not equal to 1, since there are lot other possibilities of some dressing black and some red.

2. A) Probability all four memebers will be women = 4C4 / 12C4 = 1/ 495

B) Probability all four memeber will be men = 8C4 / 12C4 = 70/495