Mathematics: Consider a problem where we are rolling 2 dices where each dice has 6 faces numbered from 1 to 6.Answer the following questions:(1) What is the sample space?(2) If the event we are interested in is the sum being 10, what would be the probability of observingsuch an event?(3) If the event we are interested in is the sum being 6, what would be the probability of observingsuch an event?

Consider a problem where we are rolling 2 dices

Ответ:

rishawn12345

02.02.2022

Mathematics

1. See Explanation for Sample Space

2. $P(10) = \frac{1}{12}$

3. $P(6) = \frac{5}{36}$

Step-by-step explanation:

Given

Roll of Two die

Solving (1): The Sample Space

Represent the first dice with S1 and the second with S2

$S_1 = \{1,2,3,4,5,6\}$

$S_2 = \{1,2,3,4,5,6\}$

The sample space of both die is:

S = (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) $(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)(55,1)(5,2)(5,3)(5,4)(5,5)(5,6)(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)}\}$

Solving (2): Probability of Sum being 10

First, we need to add the outcome of each roll in (1) above:

$S = \{2,3,4,5,6,7, 3,4,5,6,7,8, 4,5,6,7,8,9, 5,6,7,8,9,10, 6,7,8,9,10,11 7,8,9,10,11,12\}$ n(S) = 36

n(10) = 3

The required probability is:

$P(10)= \frac{3}{36}$

$P(10) = \frac{1}{12}$

Solving (3): Probability of Sum being 6

n(S) = 36

n(6) = 5

The required probability is:

$P(6) = \frac{5}{36}$

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Ответ:

lilbit217

17.07.2020

Mathematics

Teacher is 27 years old

Step-by-step explanation:

(1/2)(t - 3) = (1/3)(t + 9)

multiply by 6 to clear the fraction

3(t - 3) = 2(t + 9)

Distribute

3t - 9 = 2t + 18

Subtract 2t from both sides

t - 9 = 18

Add 9 to both sides

t = 27

Teacher is 27 years old

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