3. Applications
• Medical Field applications in estimating probability of
myocardial infarction, Cystic Fibrosis, Success rate probability
of installing a medical instrument in organs.
• Prediction of the probable life-expectancy post diagnosis of a
life threatening disorder
• Clinical trials prediction of a successful result.
• Population gender range estimation.
• Pre-polling forecasting incase of elections.
4. Examples:
Suppose there are 12 multiple choice questions, each having 5 options and
out of which only 1 correct answer per question. The probability of having
atleast one and at the most 4 correct answers is;
Probability of having exact 4 correct questions;
Interpretation
Using ‘R’ language
6. Binomial probability distribution using
a coin
Suppose a coin is thrown 10 times. The probability of throwing in a ‘heads’ and ‘tails’ is equal
i.e. ½.Now, the probability of throwing 2 heads and 8 tails is:
10C2× (½)2× (½)8 .Manually calculating this we get:
0.043.
Calculating with ‘R’, we get:
7. Understanding binominal distribution
with a text book example
• In San Francisco, 30% of workers take public
transportation daily. Sample size is 10 workers.
Probability of exactly 3 workers taking public
transport daily.
• Interpretation: 26.68% is the probability of
exact 3 workers taking public transport daily
8. • A university found that 20% of its students withdraw without completing
their introductory stats course. Assume 20 students registered for the
course.
• Scenario 1) probability that 2 or fewer withdrew.
9. Using binomial Distribution in the
Healthcare industry
• Case 1) Suppose a new medication for Ebola has
been tested for success. It has passed 3 stages of
clinical trials and all stages of pre-clinical trials
and is now to be tested on humans for its success
rate determination. The past records for the
earlier version of the medication success has
shown it to be having an 80% success rate. So for
testing the medication in a new region hit by the
epidemic can expect atleast following success
rate, using the program ‘r’
10. Interpretation: There is a 20.13% probability that exactly 7 of 10 patients
will report relief from symptoms when the probability that any one
reports relief is 80%.
Suppose, it was found that the newly developed vaccine had found to be
having a failure rate of 0.04%. So, the success rate was 0.96. In the final
clinical trials phase for 5 patients, the 100% success rate:
11. • Now, if we wanted to find out the results of no
more than 1 success for the sample size:
