5. Consider two events C and D with P(C) = 0.52 and P(D) = 0.45. If C and D are independent, thenfind the following probabilities:a) P(CND)b) P(C|D)c) P(D|C)

Answered: 5. Consider two events C and D with…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The prior probabilities for events A1 and Ag are P(A1) = 0.50 and P(A2) = 0.50. It is also known that P(A n A2) = 0. Suppose P(B|A1) = 0.10 and P(B|A2) = 0.70. a. Are events Aj and Ag mutually exclusive? Yes Explain. (i) P(A1 N A2) = 0 (ii) P(A1) + P(A2) = 1 (iii) P(A2) + P (A2 | A1) (iv) P(A2) + P(A2 | A1) choice (i) b. Compute P(A1 n B) (to 2 decimals). 0.165 Compute P(A2 N B) (to 2 decimals). 0.4819 c. Compute P(B) (to 2 decimals). 0.415 d. Apply Bayes' theorem to compute P(A1|B) (to 4 decimals). Also apply Bayes' theorem to compute P(A2|B) (to 4 decimals).
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5. Consider two events C and D with P(C) = 0.52 and P(D) = 0.45. If C and D are independent, then find the following probabilities: a) P(CND) b) P(C|D) c) P(D|C)