Question 998876
 
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)