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# Week 4 Assignment

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IMPORTANT:
Showing your work and how you reached the answer is critical in receiving your grade...simply putting down values as the final answer will not earn you any points.
Week 4 LT Assignments Chapter 5:
12. The events X and Y are mutually exclusive. Suppose P(X) _ .05 and P(Y) _ .02. What is the probability of either X or Y occurring? What is the probability that neither X nor Y will happen?

The probability of X or Y occurring is:

P(X) + P(Y) = .05 + .02 = .07

The probability of neither X or Y occurring is:

1 - .07 = .93

18. Let P(X) _ .55 and P(Y) _ .35. Assume the probability that they both occur is .20. What is the probability of either X or Y occurring?

P(XUY) = P(X) + P(Y) - P(X and Y)
P(X or Y) = 0.55 + 0.35 - 0.20 = 0.7

For any two event X and Y with P(Y) ≠ 0, the condition of probability of X given Y is as follows:

P( X ∩ Y ) = P(Y | X) x P(X) = 0.40 x 0.75 = 0.3

a. P(A1) = 3/10 = 0.3 The probability of P(A1) is 0.3/10
b. P(B1/A2) = 2/6 / 1/3 = 0.33/0.33 = 1 The probability of P(b1/A2) is 1/10
c. P(B0/A0) = 0/0 = 0 The probability of P(b0 and A0) is zero

44. Berdine’s Chicken Factory has several stores in the Hilton Head, South Carolina, area. When interviewing applicants for server positions, the owner would like to include information on the amount of tip a server can expect to earn per check (or bill). A study of 500 recent checks indicated the server earned the following amounts in tips per 8-hour shift.

Amount of Tip Number
\$0 up to \$ 20 200
20 up to 50 100
50 up to 100 75
100 up to 200 75
200 or more 50
Total 500

a. What is the probability of a tip of \$200 or more? .10 or 10%
b. Are the categories “\$0 up to \$20,” “\$20 up to \$50,” and so on considered mutually exclusive? They are mutually exclusive because the 0-20 does no effect on the 20-50 group. One group has no causal relationship on the other group. This question would make more sense if the tip amounts did not overlap (i.e; \$0-\$19, \$20-\$49….
c. If the probabilities associated with each outcome were totaled, what would that total be? \$0-\$20 | .40 | \$20-\$50 | .20 | \$50-\$100 | .15 | \$100-\$200 | .15 | \$200+ | .10 |

d. What is the probability of a tip of up to \$50? .20+.40=.60
e. What is the probability of a tip of less than \$200? .40+.20+.15+.15=.90

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