A pair of dice is rolled 3 times. What is the probability that a sum of 8 on the 2 dice will occur at least once?

QUESTION POSTED AT 01/06/2020 - 03:09 PM

Answered by admin AT 01/06/2020 - 03:09 PM

There are 36 outcomes when rolling a pair of dice.
The ones adding up to 8 are: (2,6),(3,5),(4,4),(5,3),(6,2).
 So the probability of rolling a sum of 8 is 5/36.
With three (independent) random throws, the probability of having a sum of 8 at least once equals 1-probability of no 8 at all.
P(not 8)=1-5/36=31/36
For this to happen three times, we use the multiplication rule
P(not 8 three times)=(31/36)^3=29791/46656=
P(sum of 8 at least once)=1-29791/46656=16865/46656
[=0.3615 approx.]

Post your answer

Related questions

The lengths of three sides of a quadrilateral are shown below: Side 1: 3y2 + 2y − 6 Side 2: 3y − 7 + 4y2 Side 3: −8 + 5y2 + 4y The perimeter of the quadrilateral is 4y3 + 18y2 + 16y − 26. Part A: What is the total length of sides 1, 2, and 3 of the quadrilateral? (4 points) Part B: What is the length of the fourth side of the quadrilateral? (4 points) Part C: Do the answers for Part A and Part B show that the polynomials are closed under addition and subtraction? Justify your answer. (2 points) QUESTION 2: A rectangle has sides measuring (4x + 5) units and (3x + 10) units. Part A: What is the expression that represents the area of the rectangle? Show your work to receive full credit. (4 points) Part B: What are the degree and classification of the expression obtained in Part A? (3 points) Part C: How does Part A demonstrate the closure property for polynomials? (3 points) QUESTION 3: A bucket of paint has spilled on a tile floor. The paint flow can be expressed with the function p(t) = 5t, where t represents time in minutes and p represents how far the paint is spreading. The flowing paint is creating a circular pattern on the tile. The area of the pattern can be expressed as A(p) = πp2. Part A: Find the area of the circle of spilled paint as a function of time, or A[p(t)]. Show your work. (6 points) Part B: How large is the area of spilled paint after 2 minutes? You may use 3.14 to approximate π in this problem. (4 points)

QUESTION POSTED AT 01/06/2020 - 04:46 PM

Prove that the sum of two odd functions is odd.

QUESTION POSTED AT 01/06/2020 - 04:38 PM