Question

Example 1 A fair six-sided die is rolled six times. If the face numbered k is the outcome on roll k for k=1, 2, ..., 6, we say that a match has occurred. The experiment is called a success if at least one match occurs during the six trials. Otherwise, the experiment is called a failure. The sample space S={success, failure} The event A happens when the match happens. A= {success} Assign a value to P(A)

Simulate the experiment on a computer 1000 times and guess for the result

Answer #1

A six-sided fair die is rolled six times independently. If side
i is observed on the ith roll, it is called a match on the ith
trial, i = 1, 2, 3, 4, 5, 6. Find the probabilities that
(a) all six trials result in matches,
(b) at least one match occurs in these six trials,
(c) exactly two matches occur in these six trials.

Assume that a fair
six-sided die is rolled 9 times, and the roll is called a success
if the result is in {1,2}{1,2}.
What is the probability that there are exactly 4 successes or
exactly 4 failures in the 9 rolls?

A fair die is rolled three times. We say that a match has
occurred if the outcome of the first throw is 1, or the outcome of
the second throw is 2, or the outcome of the third throw is 3. Find
the probability of the event that a match occurs.

A six-sided die is rolled 10 times and the number of times the
six is rolled is recorded. This is an example of a binomial
experiment.
Select one:
True
False

If a single six-sided die is rolled five times, what is the
probability that a six is thrown exactly three times?
a)
0.125
b)
0.032
c)
0.042
d)
0.5

Roll a single six-sided die 4 times and record the number of
sixes observed. Does the number of sixes rolled in 4 tosses of a
die meet the conditions required of a binomial random variable?
Construct the probability distribution for this experiment.

Alice rolled a fair, six-sided die ten times and counted that
she got an even number six times.
Which of the following statements is FALSE?
The distribution of the count of getting an
odd number is binomial.
The distribution of the count of getting an
even number is binomial.
The distribution of the count of getting an
even number cannot be modeled as approximately normal if the die is
rolled more than 100 times.
The distribution...

A fair 10-sided die is rolled 122 times. Consider the event
A = {the face 6 comes up at most 2 times}.
(a)
Find the normal approximation for P(A)
without the continuity correction.
(b)
Find the normal approximation for P(A)
with the continuity correction.
(c)
Find the Poisson approximation for P(A).

A 10 sided die with sides numbered 0 through 9 is rolled 5
times. Let X be the number of zeros rolled.
(a) Find the probability that exactly 2 zeros are rolled.
(b) Find the probability that no less than 4 zeros are
rolled.
(c) Find the mean and the variance of X.

PROBLEM #2
Suppose you play a game in which a fair 6 sided die is rolled
once. If the outcome of the roll (the number of dots on the side
facing upward) is less than or equal to 4, you are paid as many
dollars as the number you have rolled. Otherwise, you lose as many
dollars as the number you have rolled.
Let X be the profit from the game (or the amount of money won or
lost per...

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