Due date: Tuesday 1/20, 11:59pm
Events and outcomes
01
03
Link to originalEvents - descriptions to sets
You are modeling quality assurance for cars coming off an assembly line. They are either good (G) or broken (B). You watch 4 cars come off and record their status as a sequence of these letters, for example ‘GGBG’.
Determine the sets defined by the events having the following descriptions:
(a) “third car is broken”
(b) “all cars have the same status”
(c) “at least one car is broken”
(d) “no consecutive cars have the same status”
Solution
Probability models
02
06
Link to originalResearcher’s degree
Of 1000 researchers at a research laboratory, 375 have a degree in mathematics, 450 have a degree in computer science, and 150 of the researchers have a degree in both fields. One researcher’s name is selected at random.
(a) What is the probability that the researcher has a degree in mathematics, but not in computer science?
(b) What is the probability that the researcher has no degree in either mathematics or computer science?
Solution
03
02
Link to originalInclusion-exclusion reasoning
Your friend says: “according to my calculations, the probability of
is and the probability of is , but the probability of and both happening is only .” You tell your friend they don’t understand probability. Why?
Solution
Conditional probability
04
02
Link to originalConditioning - two dice, at least one is 5
Two dice are rolled, and at least one is a 5.
What is the probability that their sum is 10?
Solution
05
03
Link to originalConditioning - two dice, differing numbers
Two dice are rolled, and the outcomes are different.
What is the probability of getting at least one 1?
Solution
06
06
Link to originalConditioning relation
Suppose you know
and and . Calculate
and and .
Solution