Question

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 the probabilities as fractions.)

(a) 8, given that exactly one die came up 2.

(b) 6, given that exactly one die came up 2.

3.) 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) 6, given that a double was rolled

(b) a double, given that an 6 was rolled

Answer #1

1)

a) There are 36 possibilities. 18 of them are odd. Possible
outcomes with a sum of 5 are: (1,4), (4,1), (2,3) and (3,2). The
conitional probability is therefore 4/18 or 2/9.

b) If a sum of 5 is rolled, the sum is necessarily odd, so the
conditional probability is 1.

2)

a) 1/5, there are 10 possibilities where there is a 2. Two of
those ten add up to 8 . 2/10=1/5

(b) 1/5, same explanation as (a)

3)

1/5, when you roll a pair of dice, there are 36 possibilities total (6x6). Of those possibilities, only five of them add up to 6. Out of those 5, only one of them is a double

A pair of dice is rolled. Find the probabilities of the given
events. (Enter exact numbers as integers, fractions, or
decimals.)
(a) The sum is 6.
(b) The sum is 6, given that the sum is less than 8

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?

Find the probability that the sum is as stated when a pair of
dice is rolled. (Enter your answers as fractions.) (a) 8 or 11 (b)
8 or 11 or doubles

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...

If a pair of dice, one green and one red, is rolled, what is the
probability that the following will occur? (Assume both dice are
six-sided. Enter your probabilities as fractions.)
(a) Pr(3 ≤ S ≤ 4), where S is the sum rolled
(b) Pr(8 ≤ S ≤ 11), where S is the sum rolled

Suppose we roll a pair of fair dice, let A=the numbers I rolled
add up to exactly 8, and let B=the numbers I rolled multiply to an
even number. Find P(Bc|Ac)

A pair of dice is rolled. If we let x = sum of the two numbers
that show up on the uppermost face of the dice,
a) determine the probability distribution (mass function) of
x.
b) determine
1) P(x≤4) 5) P(4≤x≤8)
2) P(x<6) 6) P(4<x<8)
3) P(x>7) 7) P(x=5)
4) P(x≥3)

A pair of dice (one red and one green) is rolled. Think about
these events:
A= event that the sum of the numbers on the dice is 8
B= event that the red die shows the number 4
Find the following probabilities:
P(A)= ?
P(A ∩ B)=?
Suppose P(A) = 0.3, P(B )= 0.4, and P(A ∩ B) = 0.04
Find the following probabilities:
P(A ∩ Bc)=?
P(B ∩ Ac)=?
Please include work and answers!

1. a pair of fair dice is rolled. if the sum of the spots is 7,
determine the probability that one die showed a 2
2.what is the probability of rolling a sum of seven with a pair
of fair dice if one of them shows a five

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