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42. Consider two disjoint (or mutually exclusive) events A and B. If P(A) = 0.7 and P(B) = 0.2, find P(AUB). 43. Consider two disjoint (or mutually exclusive) events A and B with P(A) = 0.7 and P(B) = 0.4. Are these probabilities correctly assigned? (Hint: Calculate P(AUB).)

42. Consider two disjoint (or mutually exclusive) events A and B. If P(A) = 0.7 and P(B) = 0.2, find P(AUB). 43. Consider two disjoint (or mutually exclusive) events A and B with P(A) = 0.7 and P(B) = 0.4. Are these probabilities correctly assigned? (Hint: Calculate P(AUB).)

MATLAB: An Introduction with Applications
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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Q42 and 43
(a) What outcomes are in the event Ar B? (b) What outcomes are in the event BUC? (c) What outcomes are in the event C'? (d) Are the events AN B and BOA the same? Why? (e) Are the events BUC and CUB the same? Why? 41. A survey of 100 male students and 100 female students regarding their favorite Mexican food restaurant yielded the results given below. Gender Chipotle Moe's Salsaritas Qʻdoba Male 38 35 20 Female 40 30 13 17 (a) What is the probability that a respondent is male? (b) What is the probability that a respondent likes Q'doba? (c) What is the probability that a respondent likes Salsaritas and is female? (d) What is the probability that a respondent likes Salsaritas or is female? 42. Consider two disjoint (or mutually exclusive) events A and B. If P(A) = 0.7 and P(B) = 0.2, find P(AU B). 43. Consider two disjoint (or mutually exclusive) events A and B with P(A) = 0.7 and P(B) = 0.4. Are these probabilities correctly assigned? (Hint: Calculate P(A U B).) 44. Suppose P(A) = 0.60 and P(B) = 0.7. Can events A, B be disjoint? 45. It is estimated that 63% of Americans will watch the Masters golf tournament and only 48% will watch the British Open. If it is estimated that 37% of Americans will watch both tournaments, what is the probability that they will watch at least one of the golf tournaments? 46. Consider drawing two cards from a regular deck of cards (52 cards total, 4 suits, 13 cards in each suit). What is the probability that you draw two Aces if the cards are drawn (a) With replacement? (b) Without replacement?
Transcribed Image Text:(a) What outcomes are in the event Ar B? (b) What outcomes are in the event BUC? (c) What outcomes are in the event C'? (d) Are the events AN B and BOA the same? Why? (e) Are the events BUC and CUB the same? Why? 41. A survey of 100 male students and 100 female students regarding their favorite Mexican food restaurant yielded the results given below. Gender Chipotle Moe's Salsaritas Qʻdoba Male 38 35 20 Female 40 30 13 17 (a) What is the probability that a respondent is male? (b) What is the probability that a respondent likes Q'doba? (c) What is the probability that a respondent likes Salsaritas and is female? (d) What is the probability that a respondent likes Salsaritas or is female? 42. Consider two disjoint (or mutually exclusive) events A and B. If P(A) = 0.7 and P(B) = 0.2, find P(AU B). 43. Consider two disjoint (or mutually exclusive) events A and B with P(A) = 0.7 and P(B) = 0.4. Are these probabilities correctly assigned? (Hint: Calculate P(A U B).) 44. Suppose P(A) = 0.60 and P(B) = 0.7. Can events A, B be disjoint? 45. It is estimated that 63% of Americans will watch the Masters golf tournament and only 48% will watch the British Open. If it is estimated that 37% of Americans will watch both tournaments, what is the probability that they will watch at least one of the golf tournaments? 46. Consider drawing two cards from a regular deck of cards (52 cards total, 4 suits, 13 cards in each suit). What is the probability that you draw two Aces if the cards are drawn (a) With replacement? (b) Without replacement?
Expert Solution
Step 1

Q42.

If A and B are two disjoint probabilities, then we know that P[A∩B]=0, and

P[A∪B]= P[A]+P[B]-P[A∩B], so

 

P[A∪B]= P[A]+P[B], 

So, P[A∪B]= 0.7+0.2=0.9

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