## Question 325:

1

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Use the binomial probability here. We have a proportion of .20 and the phrase at most two I interpret as we want to know the cumulative probability of 0, 1 and 2 of 10 patients getting the side-effect. In other words, he gives the drug to 10 patients, what is the probability You can use the Excel formula:

=BINOMDIST(2,10,0.2,TRUE) where the true will provide the cumulative probabilities for 0, 1 and 2. You should get .6778 or the probability that no more than 2 will get a side effect is 67%. We can check this by adding up the individual probabilities for 0, 1 and 2 by just changing the excel formula to =BINOMDIST(0,10,0.2,FALSE), where the 1st value will be 0,1 then 2.

The probabilities are :

• 0: .107 (the probability exactly 0 of 10 will get a side effect is .107)
• 1: .268
• 2: .302

and the sum of these probabilities is (.017+.268+.302) = ~.677 confirming the earlier result from Excel.

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