SOLUTION: A recent study in NJ showed that 50% of all patients will return to the same dentist. Suppose nine patients are selected at random, what is the probability that: (a) Exactly five

Algebra ->  Algebra  -> Probability-and-statistics -> SOLUTION: A recent study in NJ showed that 50% of all patients will return to the same dentist. Suppose nine patients are selected at random, what is the probability that: (a) Exactly five      Log On

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 Click here to see ALL problems on Probability-and-statistics Question 627278: A recent study in NJ showed that 50% of all patients will return to the same dentist. Suppose nine patients are selected at random, what is the probability that: (a) Exactly five of the patients will return? (b) All nine will return? (c) At least eight will return? (d) At least one will return? (e) How many patients would be expected to return to the same dentist, i.e., what is the mean of the distribution?Answer by ewatrrr(10682)   (Show Source): You can put this solution on YOUR website! ``` Hi, Note: The probability of x successes in n trials is: P = nCx* where p and q are the probabilities of success and failure respectively. In this case p & q are = 1/2 or .5 nCx = (a) Exactly five of the patients will return? 9C5(.5)^5(.5)^4 (b) All nine will return? 9C9(.5)^9 (c) At least eight will return? 1 - 9C9(.5)^9 (d) At least one will return? 9C0(.5)^0(.5^9) + 9C1(.5)^1(.5)^8 (e) How many patients would be expected to return to the same dentist, i.e., what is the mean of the distribution? ```