Microfracture knee surgery has a 75% chance of success on patients with degenerative knees. The surgery is performed on three patients. Find the probability of the surgery being successful on exactly two patients. State what q is equal to.

Answer :

Given :

The probability of success $(p)=0.75$

Sample size $(n)=3$

Solution :

The probability of failure :

$$\therefore q=1–P=1–0.75=0.25$$

→ The probability of the surgery being successful on exactly two patients :

$$P(x=2)=(\genfrac{}{}{0ex}{}{n}{x})p^x(1-p{)}^{n-x}{|}_{x=2}$$ $$=(\genfrac{}{}{0ex}{}{3}{2}){0.75}^2(1-0.75{)}^{3-2}$$ $$=0.4218$$