SOLUTION: A doctor knows from experience that 18% of the patients to whom she gives a certain drug will have undesirable side effects. Among the 9 patients to whom she gives the drug, find t
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Question 1111045: A doctor knows from experience that 18% of the patients to whom she gives a certain drug will have undesirable side effects. Among the 9 patients to whom she gives the drug, find the following probabilities. (Give your answers correct to three decimal places.)
(a) Find the probability P(At most two will have undesirable side effects).
(b) Find the probability P(At least two will have undesirable side effects).
You can put this solution on YOUR website! The probability of one patient having undesirable side effects is .
The probability of one patient not having undesirable side effects is .
In a binomial distribution,
the probabilities of exactly 0, 1, and 2 out of 9 patients having undesirable side effects
would be the coefficients of the first three terms of
The first term is the probability of exactly 0 patients having undesirable side effects.
Rounding, it is .
The second term represents the probability of exactly 1 patients having undesirable side effects.
Rounding, its coefficient is .
The third term represents the probability of exactly 2 patients having undesirable side effects.
Rounding, its coefficient is .
(a) P(At most two will have undesirable side effects) = .
Presumably the teacher wants the probability as a decimal,
and the answer "correct to three decimal places" would be .
We can tell the doctor that
P(At most two will have undesirable side effects) = .
(b) P(Less than 2 patients having undesirable side effects)
= P(no undesirable side effects) + P(exactly one patient having undesirable side effects) .
The opposite of that is 2 or more patients having undesirable side effects,
or "at least two" patients having undesirable side effects, so
P(At least two will have undesirable side effects) .
the answer "correct to three decimal places" would be .
