Question
In: Statistics and Probability
A specially made pair of dice has only one- and two-spots on the faces. One of...
A specially made pair of dice has only one- and two-spots on the faces. One of the dice has three faces with a one-spot and three faces with a two-spot. The other die has two faces with a one-spot and four faces with a two-spot. One of the dice is selected at random and then rolled six times. If a one-spot shows up only once, what is the probability that it is the die with the three one-spots?
Solutions
orchestra answered 2 years agoRelated Solutions
A specially made pair of dice has only one- and two-spots on the faces. One of...
A specially made pair of dice has only one- and two-spots on
the faces. One of the dice has three faces with a one-spot and
three faces with a two-spot. The other die has two faces with a
one-spot and four faces with a two-spot. One of the dice is
selected at random and then rolled six times. If a two-spot shows
up five times, what is the probability that it is the die with the
three two-spots?
(Simplify your...
Roll two dice 48 times and record the sum of the spots on the top faces...
Roll two dice 48 times and record the sum of the spots
on the top faces as you roll. Then construct a probability
distribution for your 48 sums. Using the probability distribution,
you constructed, find the mean number of spots. (If you don't have
two dice, then cut out 6 pieces of paper with each being the same
size and with #1,2,3,4,5,6 written on them. Place the pieces of
paper in a hat or bowl. Pull out a number, then...
Shandelle rolls a pair of fair dice and sums the number of spots that appear on...
Shandelle rolls a pair of fair dice and sums the number of spots
that appear on the up faces. She then flips a fair coin the number
times associated with the sum of the spots. For example, if she
rolled a 3 and a 4, then she flips the fair coin 7 times. If the
coin flipping part of the random experiment yielded an equal number
of heads and tails, find the probability that she rolled an 8 on
the...
2. Roll a pair of unbiased dice. Let X be the maximum of the two faces...
2. Roll a pair of unbiased dice. Let X be the maximum of the two
faces and Y be the sum of the two faces. What is the joint density
of X and Y ?
A pair of dice is cast. What is the probability that the sum of the two...
A pair of dice is cast. What is the probability that the sum of
the two number landing uppermost is less than 5, if it is known
that the sum of the numbers falling uppermost is less than 7?
A gambler plays a dice game where a pair of fair dice are rolled one time...
A gambler plays a dice game where a pair of fair dice are rolled
one time and the sum is recorded. The gambler will continue to
place $2 bets that the sum is 6, 7, 8, or 9 until she has won 7 of
these bets. That is, each time the dice are rolled, she wins $2 if
the sum is 6, 7, 8, or 9 and she loses $2 each time the sum is not
6, 7, 8, or...
Two fair dice are tossed, and (X,Y) denote the number of spots on the first and...
Two fair dice are tossed, and (X,Y) denote the number of spots
on the first and on the second dice. Consider two random variables:
U = X + Y and W = | X - Y |.
A). Derive the distribution of U. List all possible values and
evaluate their probabilities.
B). Derive the distribution of W. List all possible values and
evaluate their probabilities.
C). Determine the conditional probability P[6 <= U <= 7 |
W <= 1]
Roll a pair of dice (one is red and the other is green). Let A be...
Roll a pair of dice (one is red and the other is green). Let A
be the event that the red die is 4 or 5. Let B be the event that
the green die is 1 Let C be the event that the dice sum is 7 or
8.
Calculate P(A), P(B), P(C)
Calculate P(A|C), P(A|B)
Are the events A and C independent?
Suppose box 1 has four black marbles and two white marbles, and
box 2 has two...
What is the probability that at least one of a pair of fair dice lands of...
What is the probability that at least one of a pair of fair dice
lands of 5, given that the sum of the dice is 9?
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...
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