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Probability

BUSINESS ANALYSIS

An urn contains 4 green and 6 blue chips. If the drawing of 2 chips in succession is done with replacement determine the probability of:

A. drawing 2 green chips
B. Drawing a blue chip on the first draw and a green chip on the second draw.
C. Drawing a blue chip on the first draw and a blue chip on the second.
D. Drawing a green chip on the second draw given that a blue chip was drawn on the first draw.

A.. p (green chip) 4/10 x 6/10 = 24/100 p(4) (6) = 24

B. p (blue chip) 6/10 x 4/10 = 24/100 p(6) (4) = 24

C. p (blue chip) 6/10 x6/10 = 36/100 p(6) (6)= 36

D. p (blue chip) 6/10 x 4/10 = 24/100 p(6) (4) = 36

2. An urn contains 3 yellow and 7 blue chips. If the drawing of 2 chips in succession is done without replacing the first chip drawn, determine the probability of:

A. Drawing 2 blue chips.
B. Drawing a yellow chip on the first draw and a blue chip on the second draw.
C. Drawing 2 yellow chips.
D. Drawing a yellow chip on the second draw given that a blue chip was drawn on the first draw.

A. p (blue chip) 7/10 x 6/9 = 42/90 p(7)(6) = 42

B. p (yellow chip) 3/10 x 7/9 = 21/90 p(3)(7) = 21

C. p (yellow chip) 3/10 x 2/9 = 6/90 p(3)(2) = 6

D. p (blue chip) 3/9 x 7/10 = 21/90 P(3)(7) = 21

x + 2x + 8x + 5x + = 1 16x = 1 x = 1/16

3. Our department store is having a sale on personal computers, of which three are in stock (no rain checks). There is a certain probability of selling none. The probability of selling one is twice as great as the probability of selling none. The probability of selling two is four times the probability of selling one. Finally, the probability of selling all the personal computers is five times as great as the probability of selling none. In a table list the outcomes and their probabilities.

QUANTITY DEMAND PROBABILITY

0 x 1/16

1 2x 2/16

2 8x 8/16

3 5x 15/16

p (0) = 0 / 16 x 1/16 = 1/16

p (2) = 0/16 x 2/16 = 2/ 16

p (4) = 2/16 x 4/16 = 8/16

p (3) = 3/16 x 5/16 = 15/16

4. In a production run of 260 units there are exactly 12 defective items.

A. What is the probability that a randomly selected item is defective?

B. If two items are sampled without replacement, what is the probability that both are good?

C. If two items are randomly sampled without replacement, what is the probability that the first is good but the second is defective?

A. 12/260 = 0.046 = 5%
B. 12/260 x 12/260 = 144/ 67600 = 0.0021 = 2%
C. 12/260 x 11/259 = 132/ 67340 = 0.0019 = .19

Solution Summary

The solution answers several questions below related to probability

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