Consider randomly selecting a student at a large university. Let A be the event that the selected student has a Visa card, let B be the analogous event for MasterCard, and let C be the event that the selected student has an American Express card. Suppose that P(A) = 0.6, P(B) = 0.4, and P(A n B) = 0.3, suppose that P(C) = 0.2, P(An C) = 0.14, P(B n C) = 0.1, and P(A n B n C) = 0.08. (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 Express card? (c) Calculate P(B | A) and P(A | B). P(B | A) = P(A | B) = Interpret P(B | A) and P(A | B). (Select all that apply.) O P(B | A) is the probability that given that a student has a MasterCard, they also have a Visa card. O P(A | B) is the probability that a student does not have a MasterCard or a Visa card. O P(A | B) is the probability that given that a student has a Visa card, they also have a MasterCard. O P(B | A) is the probability that given that a student has a Visa card, they also have a MasterCard. O P(B | A) is the probability that a student does not have a MasterCard or a Visa card. O P(A | B) is the probability that given that a student has a MasterCard, they also have a Visa card. (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?According to a posting on a website subsequent to the death ofa child who bit into a peanut, a certain study found that syn ofchildren younger than 18 in the United States haye at least one food allergy. Among those with food allergies, about 39% had a history of seyere reaction. [a] If a child younger than 18 is randomly selected, what is the probability that he or she has at least one food allergy and a history of seyere reaction? {Enter your answer to four decimal places.) |:| {bl It was also reported that 30% ofthose with an allergy in fact are allergic to multiple foods. If a child younger than 18 is randomly selected, what is the probability that he or she is allergic to multiple foods? {Enter your answer to three decimal places.) |:| Seyentyeight percent ofthe light aircraft that disappear while in ight in a certain country are subsequently discoyered. Of the aircraft that are discovered, 55% have an emergency locator, whereas 88% ofthe aircraft not discovered do not have such a locator. Suppose a light aircraft has disappeared. {Round your answers to three decimal places.) {a} If it has an emergency locatorI what is the probability that it will not be discovered? |:| [b] If it does not have an emergency locator, what is the probability that it will be discoyered?I |:|