Example on Conditional Probability | Don't Memorise

TL;DR

The video explains how to use conditional probability to find the probability of both children in a family being girls given certain conditions.

Transcript

so far we've understood what conditional probability is and seen a practical example wherein we use the conditional probability to predict the outcome of an event now in this video we are going to solve an example based on it if a family has two children then what is the probability that both children are girls given that in the first case at least... Read More

Key Insights

• 🆘 Conditional probability helps us calculate the probability of an event, given a certain condition.
• 👾 The sample space represents all the possible outcomes before knowing any specific condition or fact.
• #️⃣ The probability of an event can be found by dividing the number of favorable outcomes with the total number of possible outcomes.
• 🗂️ Conditional probability is calculated by dividing the probability of the intersection of two events by the probability of the condition event.

Questions & Answers

Q: What is conditional probability?

Conditional probability is used to determine the probability of an event occurring, given that another event has already occurred. It helps us make predictions based on certain conditions.

Q: How is the sample space represented in the example?

The sample space is represented by listing out all the possible outcomes, with the elder child represented by a capital letter and the younger one represented by a small letter. There are four possible outcomes in this case.

Q: How is the probability of both children being girls calculated?

Out of the four possible outcomes, only one outcome satisfies the condition of both children being girls. Therefore, the probability is calculated as 1/4.

Q: What is the conditional probability in this example?

The conditional probability being calculated is the probability of both children being girls, given the condition that at least one is a girl. It is denoted as P(e|f).

Summary & Key Takeaways

• The video discusses an example of calculating the probability of both children in a family being girls, given the condition that at least one is a girl.

• The sample space is presented, along with the representation of the events using capital and small letters.

• Using conditional probability, the video calculates the probability for both cases and concludes that the probability of both children being girls, given that at least one is a girl, is 1/3.