Probability Theory
Ankur Sinha, Ph.D.
asinha@iima.ac.in
Production and Quantitative Methods
Indian Institute of Management Ahmedabad
Some applications
A manufacturer has a large order to fulfil. To complete
the order on schedule, the assembly line needs to run
without a breakdown for the next 5 days. What is the
probability that the manufacturer will not be able to
complete the order on schedule due to breakdown in the
assembly line? Past data indicates a 95% chance that the
assembly line runs a full day without breaking down.
Ankur Sinha
Some applications
A manufacturer has a large order to fulfil. To complete
the order on schedule, the assembly line needs to run
without a breakdown for the next 5 days. What is the
probability that the manufacturer will not be able to
complete the order on schedule due to breakdown in the
assembly line? Past data indicates a 95% chance that the
assembly line runs a full day without breaking down.
In case there is a penalty for not fulfilling the orders in
time, what penalty should the manufacturer settle with?
Ankur Sinha
Some applications
For a particular type of loan, there is a 2% chance that
the borrower will default, 15% chance that the borrower
will fall behind (not pay in time), and 83% chance that
the borrower will replay the debt on schedule. What is
the chance that all the 100 borrowers will repay their
loan on time?
Ankur Sinha
Some applications
For a particular type of loan, there is a 2% chance that
the borrower will default, 15% chance that the borrower
will fall behind (not pay in time), and 83% chance that
the borrower will replay the debt on schedule. What is
the chance that all the 100 borrowers will repay their
loan on time?
How do you do the pricing of the loan?
Ankur Sinha
Some applications
An insurance salesman visits up to three clients each day,
hoping to sell a new policy. He stops for the day once he
makes a sale. Each client independently decides whether
to buy a policy; 10% of clients purchase the policy.
Ankur Sinha
Some applications
An insurance salesman visits up to three clients each day,
hoping to sell a new policy. He stops for the day once he
makes a sale. Each client independently decides whether
to buy a policy; 10% of clients purchase the policy.
• Find the expected number of clients he visits in a day.
• If the salesman earns Rs. 3,000 per policy sold, how
much can he expect to make per day?
Ankur Sinha
Some applications
Construction firm bids on a contract. It anticipates a
profit of $50,000 if it gets the contract for the full
project, and it estimates a profit of $20,000 on a shared
project. The company estimates there’s a 20% chance it
will get the larger contract and a 75 % chance it will get
the smaller contract; otherwise, it gets nothing.
Ankur Sinha
Some applications
Construction firm bids on a contract. It anticipates a
profit of $50,000 if it gets the contract for the full
project, and it estimates a profit of $20,000 on a shared
project. The company estimates there’s a 20% chance it
will get the larger contract and a 75 % chance it will get
the smaller contract; otherwise, it gets nothing.
Should the firm participate in the bid if the bidding price
is $2,000?
Ankur Sinha
Some applications
An insurance company observes from its past data that
out of 1 million house insurances that it has sold, it had
to pay an average of Rs. 100,000 per house to almost
1000 of the clients who bought the insurance. Given
that their annual costs have gone up significantly because
of increase in commercial real estate prices, they are
wondering how to price the premium.
Ankur Sinha
Some applications
An insurance company observes from its past data that
out of 1 million house insurances that it has sold, it had
to pay an average of Rs. 100,000 per house to almost
1000 of the clients who bought the insurance. Given
that their annual costs have gone up significantly because
of increase in commercial real estate prices, they are
wondering how to price the premium.
Can you help the insurance company?
Ankur Sinha
Welcome COVID-19
• Probability of getting the disease
• Accuracy of the test kit
• False positives
• False negatives
• Sensitivity of the test
• Specificity of the test
• Confusion matrix
• I tested positive, I am asymptomatic, do I have the disease?
• Poor test accuracy is not a problem for estimation, law of large
number works!
Ankur Sinha
