Three machines turn out all the products in a factory, with the first machine producing 25% of the products, the second machine 25%, and the third machine 50%. The first machine produces defective products 12% of the time, the second machine 20% of the time and the third machine 4% of the time. What is the probability that a non-defective product came from the second machine? (Round your answer to four decimal places.)

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

Charles has six songs on a playlist. Each song is by a different artist. The artists are Joey McIntyre, Whitney Houston, Aaron Carter, Shakira, Shania Twain, and Phil Collins. He programs his player to play the songs in a random order, without repetition. What is the probability that the first song is by Aaron Carter and the second song is by Joey McIntyre? Write your answer as a fraction or a decimal, rounded to four decimal places.   The probability that the first song is by Aaron Carter and the second song is by Joey McIntyre is    .

A farmer knows that 15% of the apples in his orchard have worms. He randomly selects 5 apples from the orchard. What is the probability exactly 2 of the selected apples have worms? Round to one decimal place. 0.2% 2.4% 13.8% 39.2%

In a game with a spinner, players continue making spins until they spin “End of Turn”. The “End of Turn” sector takes up 1/12 of the spinner. What is the probability that a player will be out before their fourth spin?

Friskie is having her fifth litter. The prior litters have either been three normal pups or two normal pups and a runt. Assume the probability of either outcome is 50%.

Alex, Natasha, and Juan fill orders in a fast-food restaurant. Alex incorrectly fills 20% of the orders he takes. Natasha incorrectly fills 12% of the orders she takes. Juan incorrectly fills 5% of the orders he takes. Alex fills 30% of all orders, Natasha fills 45% of all orders, and Juan fills 25% of all orders. An order has just been filled. A. If the order was filled by Juan, what is the probability that it was filled correctly? B. Who filled the order is unknown, but the order was filled incorrectly. What are the revised probabilities that Alex, Natasha, or Juan filled the order? C. Who filled the order is unknown, but the order was filled correctly. What are the revised probabilities that Alex, Natasha, or Juan filled the order?

A company receives 30% of its shipments from source A and the rest from source B. For source A, the defective rate is 10% and for source B, the defective rate is 6%. The company just receives a shipment which contains 10 items.Determine the probability that there will be one defective item.