Question

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.

Answer #1

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...

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 4-sided die is rolled 7 times.
(a)
Find the probability that the side 1 comes up exactly 3
times.
(b)
Find the probability that there is at least one side that comes
up exactly 3 times.

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

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.

A fair six-sided die has two sides painted red, 3 sides painted
blue and one side painted yellow.
The die is rolled and the color of the
top side is recorded.
List all possible outcomes of this random experiment
Are the outcomes equally likely? Explain
Make a probability distribution table for the random variable
X: color of the top side
2. If a pair of dice painted the same way as in problem 1 is
rolled, find the probability...

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

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...

#2) A six-sided die is rolled 120 times. The
data in the following table shows the results for 120
rolls:
Number of dots facing up
Frequency
Expected frequency
1
15
2
29
3
16
4
15
5
30
6
15
Fill in the expected frequencies
Use the data given to test the claim that the die is
fair (i.e. that the probabilities for each value are the...

Whenever a standard six-sided die is rolled, one of the
following six possible outcomes will occur by chance: , , , , , and
.
These random outcomes are represented by the population data
values: 1, 2, 3, 4, 5, and 6.
At the beginning of Week 4, take a random sample of size n = 9
from this population by actually rolling a standard six-sided die 9
separate times and recording your results. If you do not have
access...

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