SOLUTION: If 20% of patients treated with a type of malaria drug suffered bad reaction, find the probability in the treatment of 10 patients, 2 will suffer a bad reaction.

Question 998876: If 20% of patients treated with a type of malaria drug suffered bad reaction, find the probability in the treatment of 10 patients, 2 will suffer a bad reaction.
Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!

Problem:
20% of patients treated with a drug suffered from bad reactions.
Find probability of exactly 2 out of ten randomly chosen patients will have bad reactions after being treated with the drug.

Solution:
The problem fits in the binomial distribution because:
1. Trials are Bernoulli (exactly two possible outcomes, true or false)
2. Number of trials (n=10) is known.
3. All trials are assumed independent and random.
4. Probability of bad reaction (p=0.20) remains constant throughout the trials.
Let r=number of bad reactions out of n=10 trials.
p=0.20 (20%).
C(n,r)=number of combinations of n objects taken r at a time
=n!/(r!(n-r)!)

Then the binomial distribution gives
P(n,r,p)=C(n,r)*p^r*(1-p)^(n-r)
Substituting values,
P(10,2,0.2)=C(10,2)*(0.2^2)*((1-0.2)^(10-2))
=45(0.20^2)(0.8^8)
=0.302 (approximately)
RELATED QUESTIONS
Consider a drug that is used to help prevent blood clots in certain patients. In... (answered by CPhill)

There are 100 patients in a hospital with a certain disease. Of these, 10 are selected to (answered by Theo)

Assignment: Suppose that in a certain malarious area past experience indicates that the (answered by Boreal)

suppose that in a certain area, past experience indicates that the probability of a... (answered by ikleyn)

Use the sample data and confidence level given below to complete part (a). A drug... (answered by Boreal)

A medical treatment has a success rate of 90%. Two patients will be treated with this... (answered by KMST)

IF THE PROBABILITY THAT AN INDIVIDUAL SUFFER A BAD REACTION FROM INJECTION OF A GIVEN... (answered by solver91311)

Suppose that in a certain malarias area past experience indicates that the probability of (answered by Boreal)

The probability of flu symptoms for a person not receiving any treatment is 0.057. In a... (answered by Boreal)