Question

A study of 204 advertising firms revealed their income after taxes:

Income after Taxes	Number of Firms
Under $1 million		88
$1 million to $20 million		52
$20 million or more		64

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

The study reveals income taxes as:

Income after taxes	Number of firms
Under $1 million	88
$1 million to $ 20 million	52
$ 20 million or more	64
Total	204

1. The probability that advertising firm at random has under $ 1 million after taxes are :

P(Under $1 million) = 88/204 =0.43

2. 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 shall be

P( Between $1 million and $20 million or more than $20 mn) = 52/204 + 64/204 = 0.57

3. The rule of probability we applied was special rule of addition.
   The two events of getting income between $1 million to $20 million and $20 million or more are mutually exclusive events. Hence, by special rule of addition, the probability that either events would occur is sum of probability of both events which has been computed in b.

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