Question

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

Answer #1

Probability = Favorable outcomes / Total Outcomes

When a pair of dice is rolled, the total outcomes =
6^{2} = 36 (for n dice it is 6^{n})

_________________________________________

(a) P(Sum is an 8 or a 11)

Favorable outcomes:

Sum of 8 = (2 6) (6 2) (3 5) (5 3) (4 4) = 5 cases

Sum of 11 = (5 6) (6 5) = 2 cases

Total Favorable outcomes = 5 + 2 = 7

Therefore the required probability = **7/36 =
0.1944**

**__________________________________________**

(b) P(sum of 8 or 11 or doubles)

Favorable outcomes for 8 or 11 = 7 (as calculated in a)

Favorable outcomes for doubles = (1 1) (2 2) (3 3) (4 4) (5 5) (6 6) = 6

Total Favorable outcomes = 7 + 6 = 13

Therefore the required probability = **13/36 =
0.3611**

**______________________________________________**

A pair of dice is tossed. Find the probability that the sum on
the 2 dice is 8, given that doubles are rolled. (Enter your
probability as a fraction.)

If
a pair of dice is rolled, what is the probability of a) rolling a
sum of 8, b) rolling a sum of 3 or rolling a sum of 6, c) rolling a
sum of 4 or rolling doubles, if a pair of dice is rolled twice,
whatnis the probability of d) rolling a sum of 9 on the first roll
and rolling a sum of 2 on the second roll

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...

A pair of dice is rolled once. find the probability of obtaining
a sum of 10 or doubles (same number on both dice).

a. If p(E) = 4/7 , find o(E) and o(E').
o(E) =
o(E') =
b. 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

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

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

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
six, given that doubles are not rolled.

A pair of dice are tossed. What is the probability that doubles
are rolled, given that the sum on the two dice is less than 5?
(Round your answer to three decimal places.)

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

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