For customers purchasing a refrigerator at a certain appliance store, let A be the event that the refrigerator was manufactured in the U.S., B be the event that the refrigerator had an icemaker, and C be the event that the customer purchased an extended warranty. Relevant probabilities are below. P(A) = 0.76      P(B | A) = 0.85     P(B | A') = 0.75 P(C | A ∩ B) = 0.84 P(C | A ∩ B') = 0.61 P(C | A' ∩ B) = 0.69 P(C | A' ∩ B') = 0.32 (a) Construct a tree diagram consisting of first-, second-, and third-generation branches and place an event label and appropriate probability next to each branch.   (b) Compute P(A ∩ B ∩ C). (Round your answer to four decimal places.) (c) Compute P(B ∩ C). (Round your answer to four decimal places.) (d) Compute P(C). (Round your answer to four decimal places.) (e) Compute P(A | B ∩ C), the probability of a U.S. purchase given that an icemaker and extended warranty are also purchased. (Round your answer to four decimal places.)

Find the probability that the car needs work on either the engine, the transmission, or both. Find the probability that the car needs no work on the transmission.

b. Determine P(F or D)= P(F or D). (Type an integer or a decimal.) c. Find the probability that a randomly selected adult is male. P(male) = (Type an integer or a decimal.)

You purchase a brand new car for $15,000 and insure it. The policy pays 78% of the car's value if there is an issue with the engine or 30% of the car's value if there is an issue with the speaker system. The probability of an issue with the engine is 0.009, and the probability there is an issue with the speaker system is 0.02. The premium for the policy is p. Let X be the insurance company's net gain from this policy. (a) Create a probability distribution for X, using p to represent the premium on the policy. Enter the possible values of X in ascending order from left to right. P(X) (b) Compute the minimum amount the insurance company will charge for this policy. Round your answer to the nearest cent

S P(A/B): A Let event A = Student belongs to at least one club on campus and event B = Student participates in team sports on campus P(B|A) = ANB At AnyTown Polytechnic College, 42% of students belong to a campus club, 38% of students participate in team sports, and 5% belong to at least one campus club and participate in team sports. Compute the probabilities requested below. Round all probabilities to four decimal places, as needed. P(ANB) = P(AnB): B

For customers purchasing a refrigerator at a certain appliance store, let A be the event that the refrigerator was manufactured in the U.S., B be the event that the refrigerator had an icemaker, and C be the event that the customer purchased an extended warranty. Relevant probabilities are below. P(A) = 0.74      P(B | A) = 0.85     P(B | A') = 0.82 P(C | A ∩ B) = 0.76 P(C | A ∩ B') = 0.55 P(C | A' ∩ B) = 0.75 P(C | A' ∩ B') = 0.25 (a) Construct a tree diagram consisting of first-, second-, and third-generation branches and place an event label and appropriate probability next to each branch.   (b) Compute P(A ∩ B ∩ C). (Round your answer to four decimal places.)(c) Compute P(B ∩ C). (Round your answer to four decimal places.)(d) Compute P(C). (Round your answer to four decimal places.)(e) Compute P(A | B ∩ C), the probability of a U.S. purchase given that an icemaker and extended warranty are also purchased. (Round your answer to four decimal places.)

a and b