**Calculate the probability for the following statements. Draw the Probability tree diagram also. In a medical college of Pune (a class of 100 people), 30 % people Like to have Misal-pav on the farewell party as per the google form survey. Remaining people have chosen vadapav. Out of those who have chosen Misal-pav 50 % said that they would eat only Jain Misal pav. Well,30 % of those have chosen Vadapav, also said they would have Jain Vadapav only.**

What is the stack (percent & number) of people Who will have Jain Food (including MISal pav and Vadapav)

What is the probability of selecting a person who would eat Misal pav given that person’s diet type is Jain.

**Discussion:**

In the above question, we are discussing conditional probability and marginal probability.

**Conditional probability **is the probability of an event occurring given that another event has already occurred. It is denoted by *P*(*A*∣*B*), which is read as “the probability of event A given event B.” The formula for conditional probability is:

In simpler terms, conditional probability reflects the updated probability of event A occurring, taking into consideration that event B has already occurred. It adjusts the probability based on the information or occurrence of another event.

For example, if you have two events, A and B, the probability of A occurring might be different when you know that B has occurred compared to when you don’t have that information. Conditional probability helps quantify this change in probability based on the occurrence of another event.

**Marginal probability **refers to the probability of a single event or variable without considering the occurrence or non-occurrence of other events. It is essentially the probability of a single event, irrespective of the outcomes of other events. The term “marginal” is used because it is often presented in the margins of probability tables.

For a single event A, the marginal probability is denoted as *P*(*A*). The formula for marginal probability is straightforward:

where the sum is taken over all possible events *B**i* that could occur. In simpler terms, marginal probability represents the overall likelihood of event A happening, regardless of the different conditions or scenarios.

To illustrate, consider the following example with two events A and B:

*P*(*A*): The probability of event A occurring.*P*(*B*): The probability of event B occurring.*P*(*A*∩*B*): The joint probability of events A and B (the probability that both A and B occur).

The marginal probability of A is simply *P*(*A*), and it is not influenced by the occurrence or non-occurrence of event B. It provides a baseline probability for the individual event.

Note: The concepts related to the question is discussed in this blog for reference purposes of the students only.

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