Question

- Three dice are rolled. What is the probability that number on first die is less than the positive difference of second and third die?

Answer #1

When three dice are rolled then total 6*6*6=216 possible outcomes like as (1,1,1), (1,5,6), extra...

Given that the number on the first die is less than the positive difference of second and third die i.e.

favourable events are (1,1,3), (1,1,4), (1,1,5),(1,1,6), (1,2,4), (1,2,5), (1,2,6), (1,3,5), (1,3,6), (1,4,6), (2,1,4), (2,1,5), (2,1,6), (2,2,5),(2,2,6), (2,3,6), (3,1,5), (3,1,6), (3,2,6) ,(4,1,6).

Here one thing should be noted that condition of positive difference. There are two possibilities. One is 2nd number always greater than 3rd such that the difference between 2nd & 3rd is +ve or 3rd number always greater than 2nd such that the difference between 3rd & 2nd is +ve. I have condition 2 i.e. I supposed that 3rd number is always greater than the 2nd number.

Total no. of favourable cases= 20

Hence, the required probability= 20/216= 0.092

Two dice were rolled. Answer the questions:
I) What is the probability that the first die will have
a number that is a multiple of 4 as the outcome? (10
points)
a. 1/2
b. 1/4
c. 1/5
d. 1/6
e. None of these
II) What is the probability that the second die will
have “a number less than or equal to 2” as the outcome? (10
points)
a. 1/4
b. 1/3
c. 1/6
d. 2/3
e. None of these
III)...

A pair of dice is rolled, and the number that appears uppermost
on each die is observed. Refer to this experiment, and find the
probability of the given event. (Enter your answer as a
fraction.)
The sum of the numbers is at least 4.
A pair of dice is rolled, and the number that appears uppermost
on each die is observed. Refer to this experiment and find the
probability of the given event. (Enter your answer as a
fraction.)
One...

Two identical fair 6-sided dice are rolled
simultaneously. Each die that shows a number less than or equal to
4 is rolled once again. Let X be the number of dice that show a
number less than or equal to 4 on the first roll, and let Y be the
total number of dice that show a number greater than 4 at the
end.
(a) Find the joint PMF of X and Y . (Show your final
answer in a...

Two dice were rolled. Answer the questions:
I) What is the probability that the first die will have
a number “3” as the outcome? (10 points)
a. 1/5
b. 1/2
c. 1/6
d. 1/36
e. None of the above
II) What is the probability that the first die will have
“an odd number” as the outcome? (10 points)
a. 1/5
b. 1/2
c. 1/6
d. 1/36
e. None of the above
III) What is the probability that the sum of...

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Suppose 5 fair die are rolled simultaneously? What is the
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number?
Please include detailed steps and explanation

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dice rolled. What is the probability of obtaining a sum greater
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Your answer is :

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first die is even and the sum of the rolls is ten. are these two
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