A total of 8 popular brands of cola are to be used in a blind taste study for consumer recognition. (a) If 5 distinct brands are chosen at random from the 8 and if a consumer is not allowed to repeat any answers, what is the probability that all 5 brands could be identified by just guessing? 56 (b) If repeats are allowed in the 5 brands chosen at random from the 8, and if a consumer is allowed to repeat answers, what is the probability that all 5 brands are identified correctly just by guessing? 1 C(10,3) may be written to express 10 choose 3, and P(10,3) may be written to express 10 permute 3.

A diamond can be classified as either gem-quality or industrial-grade. Suppose that 82% of diamonds are classified as industrial-grade. (a) Two diamonds are chosen at random. What is the probability that both diamonds are industrial-grade? (b) Six diamonds are chosen at random. What is the probability that all six diamonds are industrial-grade? (c) What is the probability that at least one of six randomly selected diamonds is gem-quality? Would it be unusual that at least one of six randomly selected diamonds is gem-quality? (a) Two diamonds are chosen at random. What is the probability that both diamonds are industrial-grade? The probability is. (Round to four decimal places as needed.) (b) Six diamonds are chosen at random. What is the probability that all six diamonds are industrial-grade? The probability is. (Round to four decimal places as needed.) (c) What is the probability that at least one of six randomly selected diamonds is gem-quality? The probability is. (Round to four…

An IRS auditor randomly selects 3 tax returns fro 49 returns of which 6 contain errors. What is the probability that she selects none of those containing errors?

A box contains 40 batteries, 5 of which have low lifetimes, 30 of which have average lifetimes, and 5 of which have high lifetimes. A consumer requires 8 batteries to run an appliance and randomly selects them all from the box. What is the probability that among the 8 batteries fitted into the consumer's appliance, there are exactly 2 low, 4 average and 2 high lifetimes batteries?

I choose a random sample of 5 of 20 sofas and I find that all of them are more than $400. If only 10 of these sofas were supposed to be more than $400, what is the probability I would get 5 costing more than $400 in my sample of 5? What would that probability be if 11 of the sofas cost more than $400? Or 12 sofas costing more than $400?