Question

3 Dice are rolled, what is the probability that they are all different numbers AND one of them lands on a 6?

Answer #1

P[ there are all different numbers AND one of them lands on a 6 ] = P[ a die throwing 6 ]*P[ remaining two die throwing any number other than 6 ]*Number of ways these three numbers can be arranged

Number of ways these three numbers can be arranged = 3! = 3*2*1

P[ a die throwing 6 ] = 1/6

P[ remaining two die throwing any number other than 6 ] = (5*4)/36 = 20/36

P[ there are all different numbers AND one of them lands on a 6 ] = (6)*(1/6)*(20/36)

**P[ there are all different numbers AND one of them lands
on a 6 ] = 0.55**

5 fair 8-sided dice are rolled.
(a)
Find the conditional probability that at least one die lands on
3 given that all 5 dice land on different numbers.

4 fair 10-sided dice are rolled.
(a)
Find the conditional probability that at least one die lands on
3 given that all 4 dice land on different numbers.
(b)
True or False: If X is the sum of the 4 numbers from
one roll, and Y is the maximum of the 4 numbers from one
roll, then X and Y are independent random
variables.

5 fair 8-sided dice are rolled.
(a)
[3 marks] Find the conditional probability that at least one
die lands on 3 given that all 5 dice land on different
numbers.
(b)
[2 marks] True or False: If X is the minimum of the 5
numbers from one roll, and Y is the sum of the 5 numbers
from one roll, then X and Y are independent
random variables.

If two fair dice are rolled, what is the probability that the
sum of the numbers rolled is greater than three?

A pair of balanced dice is rolled once and the numbers on the
top of the dice are observed
Probability that the sum of the numbers on the tops of the dice
is 6 is ?
Probability that the 2nd number in the pair is larger than the
1st number is ?
Probability that the number on the top of the second die is 4 is
?
Probability that the numbers on the top of the dice are
different is...

A pair of balanced dice is rolled once and the numbers on the
top of the dice are observed.
Probability that the sum of the numbers on the tops of the dice
is 6 is?
Probability that the 2nd number in the pair is larger than the
1st number is?
Probability that the number on the top of the second die is 4
is?
Probability that the numbers on the top of the dice are
different is?

Two fair dice are rolled.
(a) Find the conditional probability doubles are rolled, given
the sum is eight.
(b) Find the conditional probability the sum is eight, given
doubles are rolled.
(c) Find the probability at least one die lands on six.
(d) Find the conditional probability at least one die lands on
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Find the indicated probability.
When a pair of dice are rolled there are 36 different possible
outcomes: 1-1, 1-2, ... 6-6. If a pair of dice are rolled 3 times,
what is the probability of getting a sum of 5 every time? Round to
eight decimal places.
0.008
0.00137174
0.0667
0.00267918

1.) Suppose a pair of dice are rolled. Consider the sum of the
numbers on the top of the dice and find the probabilities. (Enter
the probabilities as fractions.)
(a) 5, given that the sum is odd
(b) odd, given that a 5 was rolled
2.) Suppose a pair of dice are rolled. Consider the sum of the
numbers on the top of the dice and find the probabilities. (Enter
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five show different results on the up face.

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