A doctor knows from experience that 8% of the patients to whom she gives a certa

Question

A doctor knows from experience that 8% of the patients to whom she gives a certain drug will have undesirable side effects. Among the 11 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) 0.979x 0.948 (b) Find the probability P(At least two will have undesirable side effects).[Hint: apply complement rule, P(at least 2)-1-p(less than 2)-1-[P(0) + P(1)] Check if a binomial probability distribution applies or not.

Explanation / Answer

X ~ Binomial(n,p) = Binomial( 11 , 0.08)

Binomial probability distribution is

P(X) = nCx px (1-p)n-x

a)

P( X <=2) = P(x = 0) + P( x = 1) + P( x = 2 )

=11C0 0.080 0.9211 +11C1 0.081 0.9210 +11C2 0.082 0.929

= 0.948

b)

P( X >= 2) = 1 - P( X < 2 ) = 1 - P( X <= 1 )

= 1 - { P( X = 0) + P( X = 1) }

= 1 - { 11C0 0.080 0.9211 +11C1 0.081 0.9210 }

= 1 - 0.782

= 0.218

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.