Question

Asked Sep 16, 2019

Assume that every patient with a particular type of disease has probability 0.1 of being cured within a week, if the patient is given no treatment for the disease. Ten patients with that type of disease are given a new type of drug. After one week 9 out of 10 patients are cured. What is the probability of at least 9 patients being cured if the drug is assumed to have No curative effects?

Step 1

Consider *X* as the number of successes (patients being cured) out of the *n* = 10 trials (patients). That is, random variable *X *denote the number of patients being cured.

Thus, *X* has a Binomial distribution with parameters *n* = 10 and *p* = 0.1. Since *X *is a discrete random variable, *X* has a Binomial pmf (probability mass function).

The pmf of the binomial random variable with parameters* n* = 10 and *p* = 0.1 is given as follows:

Step 2

The probability that at least 9 patients being cured if the drug is assumed to have no curative effects is same as the probability that 9 or more patients being cured. That is, the required probabi...

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