For each of the following experiments describe the sample
space.
A) Three dice are rolled.
B) 5 cards are dealt from a deck.
C) Temperature in front of a building is measured.
D) A student's overall academic performance is assessed.
Three fair dice are rolled. Let S be the total number of spots
showing, that is the sum of the results of the three rolls.
a) Find the probabilities P(S = 3), P(S = 4), P(S = 17), P(S =
18).
b) Find the probability P(S ≥ 11).
Two fair dice are rolled:
a) What is the probability of an even number or a 3 on the first
die? Are these two events mutually exclusive and why?
b) What is the probability of an even number on the first die
and a 5 on the second? Is conditional probability involved in this
case? Why or why not?
Find the probability that the total number of spots showing on
200 fair dice, rolled randomly, is in the range 680 to 720. Give
your answer as a percent, without the percent sign. Describe the
details of your calculation in the previous problem. Describe the
box model (how many tickets in the box model, what numbers are on
the tickets, how many of each?). You do not have to write complete
sentences. Give the average and SD for the box....
Two fair dice are rolled and the outcomes are recorded. Let X
denotes the larger of the two numbers obtained and Y the smaller of
the two numbers obtained. Determine probability mass functions for
X and Y, and the cumulative distribution functions for X and for Y.
Present the two cumulative distribution functions in a plot.
Calculate E (2X + 2Y −8).
A pair of dice are rolled 1,000 times with the following
frequencies of outcomes:
Sum
2
3
4
5
6
7
8
9
10
11
12
Frequency
10
30
50
70
110
150
170
140
120
80
70
Use these frequencies to calculate the approximate empirical
probabilities and odds for the events a. The sum is less than 3 or
greater than 9.
b. The sum is even or exactly divisible by...
Two fair dice are rolled. What is the probability of…
a)Rolling a total of 8?
b) Rolling a total greater than 5?
c)Rolling doubles?
d)Rolling a sum of 6 or a sum of 8?
e)Rolling a sum of 4 or doubles?
f)Rolling a sum of 4 and doubles?
g)Rolling a sum of 2, 4 times in a row?