How can you roll a dice by tossing a coin? Can you use your probability knowledge? Use your conditioning skills.

Suppose, you have gone to a picnic with your friends. You have planned to play the physical version of the Snake and Ladder game. You found out that you have lost your dice. **The shit just became real!**

Now, you have an **unbiased coin **in your wallet / purse**.** You know **Probability. **

**Aapna Time Aayega**

starts playing in the background. :p

## Can you simulate the dice from the coin?

Ofcourse, you know chances better than others. :3

Take a coin.

Toss it 3 times. Record the outcomes.

HHH = Number 1

HHT = Number 2

HTH = Number 3

HTT = Number 4

THH = Number 5

THT = Number 6

TTH = Reject it, don’t ccount the toss and toss again

TTT = Reject it, don’t ccount the toss and toss again

Voila done!

**What is the probability of HHH in this experiment?**

Let X be the outcome in the restricted experiment as shown.

How is this experiment is different from the actual experiment?

This experiment is conditioning on the event A = {HHH, HHT, HTH, HTT, THH, THT}.

\(P( X = HHH) = P (X = HHH | X \in A ) = \frac{P (X = HHH)}{P (X \in A)} = \frac{1}{6}\)

Beautiful right?

Can you generalize this idea?

## Food for thought

- Give an algorithm to simulate any conditional probability.
- Give an algorithm to simulate any event with probability \(\frac{m}{2^k}\), where \( m \leq 2^k \).
- Give an algorithm to simulate any event with probability \(\frac{m}{2^k}\), where \( n \leq 2^k \).
- Give an algorithm to simulate any event with probability \(\frac{m}{n}\), where \( m \leq n \leq 2^k \) using conditional probability.

## Watch the Video here:

## Some Useful Links:

Books for ISI MStat Entrance Exam

How to Prepare for ISI MStat Entrance Exam

ISI MStat and IIT JAM Stat Problems and Solutions