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$An ordinary (fair) die is a cube with the numbers 1 through 6 on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment. Compute the probability of each of the following events. Event A : The sum is greater than 8 . Event B : The sum is an odd number. Write your answers as fractions. (a) P(A)= ◻ (b) P(B)= ◻$

An ordinary (fair) die is a cube with the numbers $1$ through $6$ on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment. $\newline$ Compute the probability of each of the following events. $\newline$ Event $A$ : The sum is greater than $8$ . $\newline$ Event $B$ : The sum is an odd number. $\newline$ Write your answers as fractions. $\newline$ (a) $P(A)=$ ◻ $\newline$ (b) $P(B)=$ ◻

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Math Problems

Precalculus

Find probabilities using the binomial distribution

Full solution

Q. An ordinary (fair) die is a cube with the numbers

1

through

6

on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment.

\newline

Compute the probability of each of the following events.

\newline

Event

A

: The sum is greater than

8

\newline

Event

B

: The sum is an odd number.

\newline

Write your answers as fractions.

\newline

(a)

P(A)=

◻

\newline

(b)

P(B)=

◻

Calculate total outcomes: Calculate the total number of possible outcomes when a die is rolled twice. Since each die has $6$ faces, the total outcomes are $6$ (for the first roll) multiplied by $6$ (for the second roll).
Identify Event A outcomes: Identify the outcomes where the sum is greater than $8$ (Event A). These outcomes are $(3,6)$ , $(4,5)$ , $(4,6)$ , $(5,4)$ , $(5,5)$ , $(5,6)$ , $(6,3)$ , $(6,4)$ , $(6,5)$ , $(3,6)$ $0$ . Count these outcomes.
Calculate probability of Event A: Calculate the probability of Event A. Divide the number of favorable outcomes by the total number of outcomes.
Identify Event B outcomes: Identify the outcomes where the sum is an odd number (Event B). These outcomes are $(1,2)$ , $(1,4)$ , $(1,6)$ , $(2,1)$ , $(2,3)$ , $(2,5)$ , $(3,2)$ , $(3,4)$ , $(3,6)$ , $(4,1)$ , $(1,4)$ $0$ , $(1,4)$ $1$ , $(1,4)$ $2$ , $(1,4)$ $3$ , $(1,4)$ $4$ , $(1,4)$ $5$ , $(1,4)$ $6$ , $(1,4)$ $7$ . Count these outcomes.
Calculate probability of Event B: Calculate the probability of Event B. Divide the number of favorable outcomes by the total number of outcomes.