Still Confused?

Try reviewing these fundamentals first

- Home
- Statistics
- Probability

Still Confused?

Try reviewing these fundamentals first

Nope, got it.

That's the last lesson

Start now and get better math marks!

Get Started NowStart now and get better math marks!

Get Started NowStart now and get better math marks!

Get Started NowStart now and get better math marks!

Get Started Now- Intro Lesson6:06
- Lesson: 1a5:54
- Lesson: 1b10:59
- Lesson: 2a13:20
- Lesson: 2b18:37
- Lesson: 316:45

Recall:

• Multiplication Rule: $P(A \;and\;B)=P(B) \cdot P(A|B)$

• Conditional Probability: $P(B|A)$ $=$ $\frac{P(A \;and\; B)}{P(A)}$

• Law of Total Probability: $P(A)=P(B_1)P(A|B_1)+P(B_2)P(A|B_2)+ \cdots+P(B_n)P(A|B_n)$

Combining all these equations we get Bayes' Rule:

$P(B|A)$ $=$ $\frac{P(A \;and\; B)}{P(A)}= \frac{P(B) \cdot P(A|B)}{P(A)}$

$=\frac{P(B) \cdot P(A|B)}{P(B_1)P(A|B_1)+P(B_2)P(A|B_2)+ \cdots+P(B_n)P(A|B_n)}$

• Multiplication Rule: $P(A \;and\;B)=P(B) \cdot P(A|B)$

• Conditional Probability: $P(B|A)$ $=$ $\frac{P(A \;and\; B)}{P(A)}$

• Law of Total Probability: $P(A)=P(B_1)P(A|B_1)+P(B_2)P(A|B_2)+ \cdots+P(B_n)P(A|B_n)$

Combining all these equations we get Bayes' Rule:

$P(B|A)$ $=$ $\frac{P(A \;and\; B)}{P(A)}= \frac{P(B) \cdot P(A|B)}{P(A)}$

$=\frac{P(B) \cdot P(A|B)}{P(B_1)P(A|B_1)+P(B_2)P(A|B_2)+ \cdots+P(B_n)P(A|B_n)}$

- IntroductionDeriving Bayes' rule
- 1.
**Bayes' Rule**

I am going to ask my boss to be my reference after applying to another job. If she gives me a good recommendation there is a 0.75 probability that I will get the job. While if she gives me a bad recommendation there is only a 0.25 probability that I will get the job. There is a 60% chance she will give me a good reference and a 40% chance she will give me a bad reference.a)What is the probability that I will get the job?b)Given that I got the job what is the probability that she gave me a good reference - 2.I have 3 bags that each contains 5 marbles.

Bag A:

Bag B:

Bag C:

2 Green

4 Green

5 Green

3 Red

1 Red

0 Red

I roll a fair die to decide which bag I will draw from. If I roll a 1,2,3 I will draw a marble from Bag A. If I roll a 4,5 I will draw from Bag B. And if I roll a 6, then I will draw a marble from bag C.a)What is the probability that I draw a red marble?b)Suppose that I drew a green marble from a bag. What is the probability that I rolled a 6? - 3.
**False Positives**

A blood test is 95% effective when diagnosing a diseased person. However this blood test also incorrectly diagnoses a healthy person 5% of the time. If 0.1% of the population actually has this disease, then what is the probability that a person has the disease given that they tested positive?

I like this, gives you hope if you get diagnosed for a serious disease

Make note of how many healthy people and how many diseased people get diagnosed. Also make a tree diagram illustrating this.

We have over 200 practice questions in Statistics for you to master.

Get Started Now