(a) Consider three baking sessions, each consisting of 20 trainees. From this group of 60 trainees,...

(a) Consider three baking sessions, each consisting of 20 trainees. From this group of 60 trainees, a group of 3 trainees is to be chosen.

i. What is the probability that all 3 trainees are in the same session?

ii. What is the probability that 2 of the 3 trainees are in the same session and the other trainee is in a different session?

(b)

Two balls are chosen randomly from a box containing 8 white, 4 red, and 2 green balls to see if you will win any money. Suppose that you win $2 for each red ball selected, you lose $1 for each blue ball selected, and you get nothing for each green ball selected. What is the probability that you will not lose any money?

(c)

A coffee machine company receives shipments of coffee machines from three factories, labelled, 1, 2 and 3. 25% of shipments come from factory 1 whose shipments contain 8% defective coffee machines. 65% percent of the shipments come from factory 2 whose shipments contain 6% defective coffee machines. The remainder of the shipments comes from factory 3 whose shipments contain 4% of defective coffee machines. The company receives a shipment, but does not know the source. A random sample of fifteen coffee machine is inspected, and three of the Coffee machines are found to be defective. What is the probability that this shipment came from factory 2?

Expert Solution

orchestra answered 2 years ago

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