A study of 207 advertising firms revealed their income after taxes: Income after
ID: 3242565 • Letter: A
Question
A study of 207 advertising firms revealed their income after taxes: Income after Taxes Number of Firms Under $1 million $1 million to $20 million 51 $20 million or more a. 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.) Probability 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.) Probability b-2. What rule of probability was applied? Rule of probability (Click to select) Special rule of addition only Either Rule of complements only References eBExplanation / Answer
(a) Income No. of firms
under 1 million 110
1 million to 20 million 51
20 million or more 46
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Total 207
P(under 1 million) = 110/207 = 0.5314
(b-1) P(between 1 million and 20 million OR 20 million or more) = P(between 1 million and 20 million) + P(20 million or more)
= 51/207 + 46/207 = 0.2464 + 0.2222 = 0.4686
(b-2)
Special rule of addition only:
Addition theorem of probability for mutually exclusine events:
P(A+B) = P(A) + P(B), if A and B are mutually exclusive.
(c) p = probability of down = 0.45
So, P(at least one of them is oprational) = 1 - P(all 3 down) = 1 - p3 = 1 - 0.453 = 1 - 0.0911 = 0.908875
(d) p = 0.78
P(all 3 on time) = 0.783 = 0.475
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