Question

Two fair dice are rolled. Find the following probabilities:

a) P(the sum of the dice is five)

b) P(the sum of the dice is not five)

Answer #1

a)

When Two dice are rolled , Number of possible outcomes = 6 x6=36

Outcomes :

(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)

(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)

(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)

(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)

(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)

(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)

Outcomes that favor the event : sum of the dice is five

(1,4)(2,3)(3,2)(4,1)

Number of outcomes that favor the sum of the dice is five = 4

P(the sum of the dice is five)

= Number of outcomes that favor the event :sum of the dice is five / total number of outcomes = 4/36 = 1/9

**P(the sum of the dice is five) = 1/9 =
0.111111**

b) P(the sum of the dice is not five) = 1 - P(the sum of the dice is five) = 1 - (1/9) = 8/9 = 0.888889

**P(the sum of the dice is not five) = 8/9 =
0.888889**

If two fair dice are rolled find the probabilities of
the following
1. sum greater than or equal to 9 given that the roll was a
double
2. a double given that the sum was strictly greater than 9

If two fair dice are rolled, find the probability that the sum
of the dice is 7, given that the sum is greater than 6.

Two fair dice are rolled and the sum rolled is recorded.
a. Find the probability that the sum is 4. b. Find the
probability that the sum is at least 4.
c. Find the probability that the sum is at most 4.

If two fair dices are rolled, find the probabilities of the
following;
a) A sum of 8 or a double(like 1−1,2−2, ect) ?

Two fair dice are rolled once. Find the probability that their
sum is 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.

In the rolling of two fair dice calculate the following:
P(Sum of the two dice is 6)= .
P(Sum of the two dice is 10)= .
P(Sum of the two dice is not 9)= .
P(Sum of the two dice is 4 or 8)= .
P(Sum of the two dice is not 5 and not 7)= .

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

It is rolled simultaneously with a red and a blue dice.
Specify the probabilities (WK) for the following events:
A: The sum of the two rolled numbers gives 6.
P (A) =
B: The red dice shows an odd number.
P (B) =
P (A∩B) =
P (A∪B) =

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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