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Still Confused?

Try reviewing these fundamentals first.

Nope, I got it.

That's that 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 Lesson: a8:46
- Intro Lesson: b7:09
- Lesson: 110:03
- Lesson: 26:54
- Lesson: 39:07

Recall:

P(*A* and *B*)=P(*A*)$\cdot$P(*B*|*A*) or equivalently, P(*A* and *B*)=P(*B*)$\cdot$P(*A*|*B*)

__The Law of Total Probability:__

*P(A)=P(A and B)+P(A and ~B)=P(B)P(A|B)+P(~B)P(A|~B)*

Or in full generality, if all of $B_1, B_2,...B_n$ include the entire sample space S, and are all pairwise mutually exclusive then:

$P(A)=P(A$ and $B_1)+P(A$ and $B_2)+ \cdots +P(A$ and $B_n)$

$=P(B_1)P(A|B_1)+P(B_2)P(A|B_2)+ \cdots + P(B_n)P(A|B_n)$

P(

Or in full generality, if all of $B_1, B_2,...B_n$ include the entire sample space S, and are all pairwise mutually exclusive then:

$P(A)=P(A$ and $B_1)+P(A$ and $B_2)+ \cdots +P(A$ and $B_n)$

$=P(B_1)P(A|B_1)+P(B_2)P(A|B_2)+ \cdots + P(B_n)P(A|B_n)$

- Introductiona)Illustrating the Law of Total Probability for two conditional eventsb)The Law of Total Probability for more than two events
- 1.
**2 disjoint mutually exclusive events**

Back Country skiers can be divided into two classes, those with avalanche training and those who have no avalanche training. An individual with avalanche training has a probability of 0.05 of getting in an avalanche, while an individual without avalanche training has a probability of 0.20 of being in an avalanche. If 75% of backcountry skiers have avalanche training and 25% of back country skiers do not, then what is the probability that a randomly selected backcountry skier will be in an avalanche? - 2.
**3 or more disjoint mutually exclusive events**

I have 3 bags that each contains 5 marbles.

Bag 1:

Bag 2:

Bag 3:

2 Green

4 Green

5 Green

3 Red

1 Red

0 Red

I choose one bag at random and draw a marble. What is the probability that I draw a green marble? - 3.Thomas is frequently late to work. If it is sunny he will be late with probability 0.15; if it rains he is late with probability 0.05. And if it snows he is late with probability 0.5 (if he shows up at all). The meteorologist has predicted there is a 50% it will be sunny tomorrow, a 35% chance it will rain and a 15% chance it will snow. What is the probability that Thomas will be late tomorrow?

Make jokes about taking sick days + make pictures for the sun, rain and snow.