A system is made up of three components that operate independently from one another. For the system to function (work), at least two of its components must function. Suppose that the probability that component no. 1 functions equals to 0.95, component no. 2 functions equals to 0.9, and component no. 3 functions equals to 0.8. Given that the system functions, what is the probability that exactly two components function? O a. 0.967 O b. 0.293 O c. 0.034 O d. 0.98

If a household has at least one cat, there is a 30% probability that the household has at least one dog. Thirty percent of households have at least one cat and 33% of households have at least one dog. Given that a household has at least one dog, the probability that the same household has at least one cat is ________.

Q7 A faculty member meets two students in Paris, one of whom arrives by train from Amsterdam and the other from Brussels at approximately the same time. The probability that the train from Amsterdam will arrive on time is 0.93. The probability that the train from Brussels will arrive on time is 0.89, and the probability that both trains will arrive on time is 0.87. What is the probability that at least one train will arrive on time?

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