Question

A certain prescription drug is known to produce undesirable side effects in 20% of all patients who use the drug. Among a random sample of six patients using the drug, find the probability of the stated event.The probability of four patients having undesirable side effects among a random sample of six is?

Answer 1

Given the question in the question tab, the following are the solution steps to get the desired probability

Step 1: Write the given parameters

`\begin{gathered} Binomial\text{ Problems with n=6} \\ p(undesirable\text{ side effects)}=(20)/(100)=0.2 \\ p(desirable\text{ side effect)=1}-p(side\text{ effects)}=1-0.2=0.8 \end{gathered}`

Step 2: State the formula for the Binomial Distribution Model

`P(X\text{ successes})=^nC_x* p^x*(1-p)^((n-x))`

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

`\begin{gathered} n=6,x=4,p=p(\text{side effects)=0.2,}1-p=0.8 \\ P(x=4)=^6C_4*0.2^4*0.8^(6-4) \\ P(x=4)=^6C_4*0.2^4*0.8^2\Rightarrow P(x=4)=15*0.2^4*0.8^2 \\ P(x=4)=0.01536 \end{gathered}`

Hence, the probability of four patients having undesirable side effects among a random sample of six is 0.01536