01
Bayes’ 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
04
(1) Define events.
Let
be the event that she watches it. Let
be the event that the computer is stolen. We are given the probabilities
, , . We are asked to compute
.
(2) Set up formula
using Bayes’ Theorem.
(3) Plug in values.
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02
Bayes’ Theorem - Inferring die from roll
A bag contains one 4-sided die, one 6-sided die, and one 12-sided die. You draw a random die from the bag, roll it, and get a 4.
What is the probability that you drew the 6-sided die?
Solution
05
(1) Define events.
Let
be the event in which you draw the 4-sided die, be the event in which you draw the 6-sided die, and be the event in which you draw the 12-sided die. We are asked to compute
.
(2) Define obvious probabilities.
.
.
.
.
(3) Use Bayes’ Theorem to set up the formula for
.
(4) Plug in values and solve.
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03
Bayes’ Theorem - DNA evidence
A crime is committed in a town of 100,000 citizens. After all 100,000 citizens’ DNA is analyzed, your friend Jim is found to have a DNA match to evidence at the scene. A forensics expert says that the probability of a random person matching this evidence is 0.01%. How likely is it that Jim is guilty?
Solution
01
(1) Define events.
Let
be the event that Jim is guilty. Let
be the event in which the DNA matches. We are given that
. We know that
. Since there are 100,000 citizens,
, . We are asked to compute
.
(2) Use Bayes’ Theorem to set up the formula for
.
(3) Plug in values.
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