SOLUTION
Given the question in the question tab, the following are the solution steps to get the desired probability
Step 1: Write the given parameters
[tex]\begin{gathered} Binomial\text{ Problems with n=6} \\ p(undesirable\text{ side effects)}=\frac{20}{100}=0.2 \\ p(desirable\text{ side effect)=1}-p(side\text{ effects)}=1-0.2=0.8 \end{gathered}[/tex]Step 2: State the formula for the Binomial Distribution Model
[tex]P(X\text{ successes})=^nC_x\times p^x\times(1-p)^{(n-x)}[/tex]where n is the number of events
x is the required number of event
Step 3: Find the probability of four patients having undesirable side effects among a random sample of six
[tex]\begin{gathered} n=6,x=4,p=p(\text{side effects)=0.2,}1-p=0.8 \\ P(x=4)=^6C_4\times0.2^4\times0.8^{6-4} \\ P(x=4)=^6C_4\times0.2^4\times0.8^2\Rightarrow P(x=4)=15\times0.2^4\times0.8^2 \\ P(x=4)=0.01536 \end{gathered}[/tex]Hence, the probability of four patients having undesirable side effects among a random sample of six is 0.01536
