An urn contains six red balls and two blue ones. We make two...

Name: Problem 8, Chapter 12: Higher Level Mathematics
Uploaded: 2020-05-14T18:09:03-08:00
Duration: 2 min 46 s
Channel: Julian Wong
Description: An urn contains six red balls and two blue ones. We make two draws and each time we put the ball back after marking its colour. a) What is the probability that at least one of the balls is red? b) Given that at least one is red, what is the probability that the second one is red? c) Given that at least one is red, what is the probability that the second one is blue?

An urn contains six red balls and two blue ones. We make two draws and each time we put the ball back after marking its colour. a) What is the probability that at least one of the balls is red? b) Given that at least one is red, what is the probability that the second one is red? c) Given that at least one is red, what is the probability that the second one is blue?

An urn contains six red balls and two blue ones. We make two draws and each time we put the ball back after marking its colour.
a) What is the probability that at least one of the balls is red?
b) Given that at least one is red, what is the probability that the second one is red?
c) Given that at least one is red, what is the probability that the second one is blue?

Key Concepts

Probability with Replacement

When items are drawn 'with replacement', the drawn item is returned to the original set after each draw, thereby keeping the probabilities unchanged for each draw. This process ensures that every trial is identical and independent, simplifying the calculation of probabilities across multiple draws.

Independent Events

This concept refers to events whose outcomes do not affect each other. In probability theory, when events are independent, the probability of their joint occurrence is the product of their individual probabilities. This is particularly relevant when each draw or trial, such as drawing with replacement, does not change the conditions or probabilities for subsequent draws.

Conditional Probability

Conditional probability deals with finding the likelihood of an event occurring given that another event has already occurred. It refines the probability measure by restricting the sample space to the outcomes that satisfy the known condition, allowing you to compute updated probabilities based on additional information.

Complement Rule

The complement rule is a technique in probability that helps calculate the probability of an event by subtracting the probability of its complement from one. This approach is especially useful when it is easier to compute the probability of the event not happening rather than directly computing the desired event.

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