Please print this and submit this original document with your answer on the blan

Question

Please print this and submit this original document with your answer on the blanks provided. Any pertinent work should be done on another sheet of paper and submitted also. The total score of home works will be reweighted to follow the distribution given in the syllabus. Q1. The following table lists the joint probabilities associated with mammogram and breast cancer among women. One female is selected at random. What is the probability of the following events? (4 points in total, 1 for each blank) Mammogram 0.05 0.1 No ma Breast Cancer No Breast Cancer 0.01 0.84 She got mammogram She doesn't have breast cancer She has breast cancer given she has mammogram She has breast cancer given she doesn't have mammogram A. B. C. D. Q2. Suppose that A and B are two mutually exclusive events for which P(A) 0.3 and P(B) 0.4. Find each of the following: (4 points in total, 1 for each) A. PAI B)- 0.8 C. P(AU B) = 0: 7

Explanation / Answer

Q1.
a) P(she got mammogram) = 0.05+0.1 = 0.15

b) P(She doesn't have breast cancer) = 0.1 + 0.84 = 0.94

c) P(She has breast cancer / She has mammogram)
= P(She has breast cancer and has mammogram) / P(She has mammogram)
= 0.05 / 0.15 = 0.3333

d) P(She has breast cancer / she doesn't have mammogram)
= P(She has breast cancer and she doesn't have mammogram) / P( she doesn't have mammogram)
= 0.01 / 0.85 = 0.011764

Q2)
a) P(A/B) = P(A and B) / P(B)
= 0 / 0.4 since A and B are mutually exclusive i.e. P(A and B) = 0
= 0
b) P(B/A) = P(A and B) / p(A)
= 0 / 0.3 since A and B are mutually exclusive i.e. P(A and B) = 0
= 0
c) P(A U B) = P(A) + (B)
= 0.3 +0.4 =0.7
d) P(A and B) = 0

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