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Law of total probability
- Intro Lesson: a8:46
- Intro Lesson: b7:09
- Lesson: 110:03
- Lesson: 26:54
- Lesson: 39:07
Law of total probability
Lessons
Recall:
P(A and B)=P(A)⋅P(B|A) or equivalently, P(A and B)=P(B)⋅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 B1,B2,...Bn include the entire sample space S, and are all pairwise mutually exclusive then:
P(A)=P(A and B1)+P(A and B2)+⋯+P(A and Bn)
=P(B1)P(A∣B1)+P(B2)P(A∣B2)+⋯+P(Bn)P(A∣Bn)
P(A and B)=P(A)⋅P(B|A) or equivalently, P(A and B)=P(B)⋅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 B1,B2,...Bn include the entire sample space S, and are all pairwise mutually exclusive then:
P(A)=P(A and B1)+P(A and B2)+⋯+P(A and Bn)
=P(B1)P(A∣B1)+P(B2)P(A∣B2)+⋯+P(Bn)P(A∣Bn)
- 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.