Xác suất có điều kiện (Conditional probability) | Công thức nhân xác suất

Summary

This video introduces the concept of conditional probability, explaining how to calculate the probability of an event happening given that another event has occurred. It contrasts independent events with dependent events, using classic examples like coin flips, dice rolls, and heart disease to demonstrate the calculation of probabilities. The video also covers how the sample space is reduced when certain events happen and provides step-by-step explanations for solving problems, including calculating the probability of drawing two red balls from a bag. The tutorial is designed to make these concepts clear and easy to grasp.

Takeaways

• 😀 Probability is often introduced through classic experiments like tossing a coin, rolling a dice, or drawing marbles from a bag.
• 😀 Independent events occur when the outcome of one event does not affect the other, and the probability of both events happening is the product of their individual probabilities.
• 😀 Conditional probability is introduced when two events are not independent. It calculates the probability of one event occurring, given that the other has already occurred.
• 😀 In the case of independent events like coin flips or dice rolls, the probability of both events occurring is simply the product of their individual probabilities.
• 😀 An example of independent events is when two people shoot at a target, with each having a given probability of hitting it. The probability of both hitting the target is the product of their individual probabilities.
• 😀 If events A and B are not independent, we cannot use the simple multiplication rule. Instead, we must use conditional probability to account for the relationship between the events.
• 😀 The formula for conditional probability is the probability of the intersection of events A and B, divided by the probability of event B. This formula is valid only when the probability of event B is greater than 0.
• 😀 The probability multiplication formula states that the probability of two events A and B occurring is equal to the probability of A times the probability of B given A.
• 😀 Conditional probability can be illustrated visually with a sample space, where the sample space is reduced to event B, and we calculate the probability of A within that reduced sample space.
• 😀 In the example of rolling a dice, the conditional probability of event A occurring given that event B has occurred is calculated by counting the elements common to both events and dividing by the total number of elements in event B.

Q & A

What is the primary focus of this video?

The video focuses on explaining the concept of probability, specifically conditional probability, and how it differs from simple independent event probability.

Why are examples involving coins, dice, and marbles commonly used in probability?

These examples are classic because they provide simple, clear scenarios that help in building foundational concepts about probability.

What does the video explain about the probability of independent events?

For independent events, the probability of both events happening is calculated by multiplying the probability of each event occurring individually.

What happens when two events are not independent, according to the video?

When two events are not independent, the formula for calculating the combined probability changes, as the occurrence of one event affects the probability of the other event.

What is conditional probability, and how is it calculated?

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

What is the probability multiplication formula discussed in the video?

The probability multiplication formula is P(A and B) = P(A) * P(B|A), where P(B|A) is the conditional probability of event B given event A.

Can the conditional probability formula be applied when the probability of event B is zero?

No, the conditional probability formula does not work if the probability of event B is zero, as division by zero is undefined.

What example is used in the video to explain conditional probability involving dice?

The video uses a dice example where event A consists of numbers 1, 2, 3, 4, and 5, and event B consists of numbers 3, 4, 5, and 6. It demonstrates how the probability of event A, given that event B has occurred, is 3/4.

How is conditional probability applied in the second example with a bag of balls?

In this example, after drawing a red ball first, the probability of drawing a red ball a second time is calculated as 1/4, considering the reduction in the number of balls in the bag.

What is the probability of drawing two red balls from a bag containing 2 red and 3 green balls, without replacement?

The probability of drawing two red balls is calculated by multiplying the probabilities of drawing a red ball the first and second times. The result is 1/10.