onsider randomly selecting a student at a large university. Let A be t Black Men
ID: 3046926 • Letter: O
Question
onsider randomly selecting a student at a large university. Let A be t Black Mena for Goog he event that the selected student has a Visa card, let B be the analogous event for Express card. Suppose that PKA)-0.6, P(B) -0.4, and PAn B)- 0.3, suppose that PKC)-0.2, PAn-0.11, PB n g) .1, and MasterCard, and let C be the event (a) What is the probability that the selected student has at least one of the three types of cards? (b) What is the probability that the selected student has both a Visa card and a MasterCard but not an American E xpress card? (c) Calculate A) and P(A e). Interpret A) and PA , a). (Select all that apply.) I A) is the probability that given that a student has a MasterCard, they also have a visa card. PAIB) is the probability that given that a student has a MasterCard, they also have a Visa card PA 1 B) is the probability that given that a student has a Visa card, they also have a MasterCard PLA C is the probability that a student does not have a MasterCard or a Visa card A) is the probablity that given that a student has a Visa card, they also have a MasterCard A) is the probability that a student does not have a MasterCard or a Visa card O B (d) If we learn that the selected student has an American Express card, what is the probability that she or he also has both a Visa card and a MasterCard? (e) Given that the selected student has an American Express card, what is the probability that she or he has at least one of the other two types of cards?Explanation / Answer
A) P(A U B U C) = P(A ) +P(B) + P(C) - P( A and B) - P(B and C ) - P(C and A) + P(A and B and C)
= 0.6 + 0.4 + 0.2 - 0.3 - 0.1 - 0.11 + 0.07 = 0.76
b) Probability = P(A and B) - P(A and B and C)
= 0.3 - 0.07 = 0.23
c)P(B|A) = P(B and A)/P(A)
= 0.3/0.6 = 0.18
P(A|B) = P(A and B)/P(B)
= 0.3/0.4 = 0.75
OPTION -B and Option - E are correct answer.
D) P(A and B)|P(C) = P(A and B and C)/P(C)
= 0.07/0.2 = 0.35
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