# Interperting a solution involving conditional probability.

• torquerotates
Monday.In summary, the probability that a family consisting of a father, mother, and child, all born on different days, when the father was born on a Monday, is 30/49. This is calculated by taking the number of possibilities for all three being born on different days, divided by the number of possibilities for the father being born on a Monday. The total number of possibilities for the father, mother, and child is 49, and the total number of possibilities for just the father being born on a Monday is 7*7=49.

## Homework Statement

a family consisting of a father, mother, and a child is chosen at random and is asked on what day of the week each of them was born. What is the probability that all three were born on different days given that the father was born on a monday?

Solution: A is the even all three were born on different days. B is the event that the father was born on a monday. n(A and B)=6P2=30 and n(B)=7*7=49. So P(A|B)=30/49

## Homework Equations

P(A|B)=P(A and B)/P(B).
P(A|B) reads: probability of A given B.

## The Attempt at a Solution

Really, what i don't get is why for n(B), we get 7*7. I mean it should be 52 since there are 52 weeks in a year=>52 mondays in a year. I just don't get the solution that was given.

n(B) is the number of possibilities for the days for the father, mother, and child, without requiring that all three be born on different days, given that dad was born on Monday. So, 1 choice for dad, 7 choices for mom, 7 choices for kid. 1*7*7=49.

n(A and B) is 1*6P2

## 1. What is conditional probability?

Conditional probability is the likelihood of an event occurring, given that another event has already occurred. It is calculated by dividing the probability of both events occurring by the probability of the first event occurring.

## 2. How do you interpret a solution involving conditional probability?

To interpret a solution involving conditional probability, you must understand what the given events are and which one is the condition. You can then use the formula for conditional probability to calculate the likelihood of the second event occurring given the first event has already occurred.

## 3. What is the difference between conditional probability and regular probability?

The main difference between conditional probability and regular probability is that conditional probability takes into account the occurrence of a specific event, while regular probability does not. In conditional probability, the probability of an event is calculated with the additional knowledge that another event has already occurred.

## 4. How can conditional probability be useful in real-world applications?

Conditional probability is useful in real-world applications because it allows us to make predictions and decisions based on previous events. It is commonly used in fields such as statistics, machine learning, and data analysis to make informed decisions and draw conclusions from data.

## 5. What are some common misconceptions about conditional probability?

One common misconception about conditional probability is the belief that the probability of an event occurring is always increased when another event has already occurred. This is not always the case, and the actual probability depends on the specific events and their relationship. Another misconception is that conditional probability is only applicable to two events, when in reality it can be used for multiple events as well.

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