Question
In: Statistics and Probability
Two fair dice are tossed, and the up face on each die is recorded. Find the...
Two fair dice are tossed, and the up face on each die is recorded. Find the probability of observing each of the following events:
A: { The sum of the numbers is even }
B: { A 4 appears on at least one of the dice }
C: { The difference of the numbers is 2 or less }
Solutions
orchestra answered 2 years agoRelated Solutions
Two fair dice are tossed, and the face on each die is observed. Use a tree...
Two fair dice are tossed, and the face on each die is
observed.
Use a tree diagram to find the 36 sample points contained in the
sample space.
Assign probabilities to the sample points in part a.
Find the probability of each of the following events:
A = {3 showing on each die}
B = {sum of two numbers showing is 7}
C = {sum of two numbers showing is even}
Also, for events A, B, and C, which one...
Two fair dice, one blue and one red, are tossed, and the up face on each...
Two fair dice, one blue and one red, are tossed, and the up face
on each die is recorded. Define the following events:
E:E: {{ The sum of the numbers is even }}
F:F: {{ The difference of the numbers is 3 or more
}}
Find the following probabilities:
P(E)=
P(F)=
P(EandF)=
P(E|F)=
P(F|E)=
Q2. Two fair dice are tossed and recorded (a) What is the probability that the sum...
Q2. Two fair dice are tossed and recorded
(a) What is the probability that the sum of the two dice is at most
10?
(b) Given that the sum is an even number, what is the
probability that the sum of two dice is 6 or 10?
Two fair coins and a fair die are tossed. Find the sample space of the experiment...
Two fair coins and a fair die are tossed. Find the sample space
of the
experiment (10 pts); Find the probabilities of the following
events:
A- ”the die shows 2 or 3” (5 pts);
B- ”one of the coins is head, the other - tail, and the die shows
an odd number” (5
pts).
Are the events A and B independent? (5 pts).
Give proofs.
Three fair dice (black, white and red) are tossed simultaneously and the value recorded as an...
Three fair dice (black, white and red) are tossed simultaneously
and the value recorded as an ordered triple y = (yb, yw, yr), which
is a point in S.
Let A1, A2, A3 be the events A1 = {(yb, yw, yr) : yb = yw} A2 =
{(yb, yw, yr) : yb = yr} A3 = {(yb, yw, yr) : yw = yr}
(i) What is the sample space S for this experiment? How many
points or elementary events does...
Three fair dice (black, white and red) are tossed simultaneously and the value recorded as an...
Three fair dice (black, white and red) are tossed simultaneously
and the value recorded as an ordered triple y = (yb, yw, yr), which
is a point in S.
Let A1, A2, A3 be the events A1 = {(yb, yw, yr) : yb = yw} A2 =
{(yb, yw, yr) : yb = yr} A3 = {(yb, yw, yr) : yw = yr}
For the set-up described in the preceding question, let 1 ≤ t ≤
18 be a positive...
Find the probability that: Rolling a fair die 3 times, at least two dice are less...
Find the probability that:
Rolling a fair die 3 times, at least two dice are less than
4.
Previous answers have suggested 0.875 (189 feasible cases/ 216
total cases). However, from simple trial and error we can see that
there are more than 27 cases where this answers fails. For example
is the first dice gets a 4 and the 2nd dice gets 4,5,6 and the last
dice gets any number, there is already 18 cases here that are not...
Two fair dice are tossed. Let A be the maximum of the two numbers and let...
Two fair dice are tossed. Let A be the maximum of the two
numbers and let B be the absolute difference between the two
numbers. Find the joint probability of A and B. Are A and B
independent? How do you know?
Roll two fair dice. Each die has six faces. A. Let A be the event that...
Roll two fair dice. Each die has six faces.
A. Let A be the event that either a 3 or 4 is rolled first
followed by an odd number. P(A) = Round your answer to
two decimal places.
B. Let B be the event that the sum of the two dice is at most 7.
P(B) = Round your answer to two decimal places.
C. Are A and B mutually exclusive events? (Yes or No)
D. Are A and B independent or...
Find the conditional probability, in a single roll of two fair 6-sided dice, that neither die...
Find the conditional probability, in a single roll of two fair
6-sided dice, that neither die is a
three,given that the sum is greater than 7.
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