Due date: Sunday 1/25, 11:59pm
Conditional probability
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Link to originalConditional probability - algebra games
Assume that
, , and partition the sample space, and assume this data:
Find these values:
Solution
Bayes’ Theorem
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Link to originalBayes’ Theorem - Stolen computer
Someone in a coffee shop “promises” to watch your computer while you’re in the bathroom.
- If she does watch it, the probability that it gets stolen is 10%.
- If she doesn’t watch it, the probability that it gets stolen is 70%.
- You think there’s a 90% chance she is honest enough to watch it, having promised.
When you come back from the bathroom, the computer is gone.
What is the probability that she witnessed the theft?
Solution
Independence
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Link to originalIndependence algebra
Assume
, , and are mutually independent. Compute in terms of , , and .
Solution
Tree diagrams
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Link to originalBin of marbles
A bin contains 5 red marbles, 7 blue marbles, and 3 white marbles.
We draw a random marble. If it’s red, we put it back, if it’s not red, we keep it. We do this three times.
(a) What is the probability of getting red then white then blue?
(b) Suppose the last draw was blue. What is the probability that the first was red?
Solution
Counting
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Link to originalCounting license plates
A license plate must consist of 3 letters followed by 4 digits. Assuming we choose from 26 letters, A-Z, and 10 digits, 0-9, how many different license plates could be created if:
(a) Letters and numbers cannot be repeated.
(b) Letters and numbers can be repeated except that there must be exactly two 9’s.
Solution
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Link to originalCounting outcomes - permutations and combinations
In a lottery, five distinct numbers are picked at random from
. How many possible outcomes are there: (a) If we care about the order of numbers.
(b) If the order does not matter.
Solution