Question

A study of 248 advertising firms revealed their income after taxes:

Income after Taxes	Number of Firms
Under $1 million		132
$1 million to $20 million		63
$20 million or more		53

1. What is the probability an advertising firm selected at random has under $1 million in income after taxes? (Round your answer to 2 decimal places.)

1. b-1. What is the probability an advertising firm selected at random has either an income between $1 million and $20 million, or an income of $20 million or more? (Round your answer to 2 decimal places.)

1. b-2. What rule of probability was applied?

• Rule of complements only

• Special rule of addition only

• Either

Answer 1

a) Classical probability is calculated by the ratio of the number of trials favourable to the event to the total number of trials

Probability that an advertising firm selected at random has under $1 million in income after taxes = 132/248 = 0.53

b) Rule of complements states

Special rule of addition states that if A and B are mutually exclusive then P(A or B) = P(A) + P(B)  

The probability that an advertising firm selected at random has either an income between $1 million and $20 million or an income of $20 million or more = (63+53)/248 = 0.47

The above solution can also be obtained by the rule of complements

The probability that an advertising firm selected at random has either an income between $1 million and $20 million or an income of $20 million or more = 1 - Probability that an advertising firm selected at random has under $1 million in income after taxes = 1 - 0.53 = 0.47

Therefor either of the rules can be used.