Math Problem Statement

A standard die has 6 sides numbered 1 through 6. What is the best and most specific way of computing the probabilities of outcomes from rolling a pair of standard dice?

 one-step fraction or division: 

number specified

total number

list or fraction or division of pairs: 

number specified pairs

total pairs

    use tree or multiplication rule: 

P(A ∩ B) = P(A | B) · P(B)

box, Venn diagram, complement rule: 

1-P(A)

, or addition rule: 

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

conditional probability formula: 

P(A|B) = 

P(A∩ B)

P(B)

permutation(s): 

n!

(nk)!

combination(s): 

n!

(nk)k!

other factorial(s): 

n!

exponent(s): 

pn

What is the probability that the sum of the numbers showing is: (a) at most 3 ? Write answer as a reduced fraction. 

(b) exactly 6 ? Write answer as a reduced fraction. 

(c) at least 9 ? Write answer as a reduced fraction.

Solution

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Math Problem Analysis

Mathematical Concepts

Probability
Combinatorics

Formulas

P(A ∩ B) = P(A | B) · P(B)
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
Conditional probability formula: P(A | B) = P(A ∩ B) / P(B)

Theorems

Multiplication rule
Addition rule
Complement rule

Suitable Grade Level

Grades 6-8