Question 1210436: Round each answer to at least 4 decimal places accuracy.
Owen, the inventory manager at a company's distribution center, records the following inventory for a beach towel that comes in two sizes (large or small) and three colors (Green, Black, and Yellow).
Green Black Yellow Total
Large 18 5 3 26
Small 7 13 2 22
Total 25 18 5 48
a. If Owen selects one beach towel at random, what is the probability that the beach towel is Black or Yellow?
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b. If Owen selects one beach towel at random, what is the probability that it is Small, given that it is Green?
c. If Owen selects one beach towel at random, what is the probability that the beach towel is Black or that it is Large?
d. If Owen selects one beach towel at random, Find P(Black)?
Answer by n2(8)   (Show Source):
You can put this solution on YOUR website! .
Round each answer to at least 4 decimal places accuracy.
Owen, the inventory manager at a company's distribution center, records the following inventory for a beach towel
that comes in two sizes (large or small) and three colors (Green, Black, and Yellow).
Green Black Yellow Total
Large 18 5 3 26
Small 7 13 2 22
Total 25 18 5 48
(a) If Owen selects one beach towel at random, what is the probability that the beach towel is Black or Yellow?
(b) If Owen selects one beach towel at random, what is the probability that it is Small, given that it is Green?
(c) If Owen selects one beach towel at random, what is the probability that the beach towel is Black or that it is Large?
(d) If Owen selects one beach towel at random, Find P(Black)?
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(a) We should add the totals in columns "Black" and "Yellow", 18 + 5 = 23, and relate it
to the global total, which is 48. We get
P = 23/48 = 0.4792 (rounded)).
(b) This question is about the conditional probability.
To answer, we reduce our scope to the green towels (their number is 25, 1st column),
take the number of 'small' of them, which is 7), and relate one number to the other
P = 7/25 = 0.28. <<<---=== this number is not approximate: it is an exact number.
(c) The favorable set is the union of two subsets.
One subset is "Black" (2nd column, the total 18).
Other subset is "Large" (1st line, the total 26).
Their intersection is the cell (1,2) of 5 towels.
So, the favorable set is of 18 + 26 - 5 = 39 towels, and we relate it to the global total 48
P = 39/48 = 0.8125. (exact value)
(d) Here P(black) is the total of column "Black', which is 18, related to the global total of 48
P = 18/48 = 3/8 = 0.375 (exact value).
Solved in full: all questions are answered with explanations.
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