W01 Homework A

01

01

Sample 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?

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02

02

Sample 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?

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03

01

Venn diagrams - set rules and Kolmogorov additivity

Suppose we know three probabilities of events: $P[A]=0.4$, $P[B]=0.3$, and $P[A\cap B]=0.1$.

Calculate: $P[A\cup B]$, $P[A^c]$, $P[B^c]$, $P[A\cap B^c]$, and $P[(A\cap B{)}^c]$.

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04

04

At least two heads from three flips

A coin is flipped three times.

What is the probability that at least two heads appear?

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05

01

Conditioning

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?

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