Due date: Thursday 1/15, 11:59pm
Events and outcomes
01
01
Link to originalSample space - roll a die, flip a coin
A normal 6-sided die is cast, and then a coin is flipped. All results are recorded.
(a) Define a sample space for this experiment.
(b) How many possible events are there?
Solution
02
02
Link to originalSample space - roll a die then flip coin(s)
A normal 6-sided die is cast. If the result is even, flip a coin two times; if the result is odd, flip a coin one time. All results are recorded.
(a) Define a sample space for this experiment.
(b) How many possible events are there?
Solution
Probability models
03
01
Link to originalVenn diagrams - set rules and Kolmogorov additivity
Suppose we know three probabilities of events:
, , and . Calculate:
, , , , and .
Solution
04
04
Link to originalAt least two heads from three flips
A coin is flipped three times.
What is the probability that at least two heads appear?
Solution
Conditional probability
05
01
Link to originalConditioning
Student test-passing rates, by year:
1st year 2nd year 3rd year 4th year Pass 0.155 0.340 0.255 0.160 Fail 0.025 0.040 0.015 0.010 What is the likelihood that a randomly chosen 4th-year student passed the test?
What about for 1st-year students?
Solution