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### Practice

Suppose the numbers from 1 to 20 are written on 20 slips of paper and put into a bowl. You draw a slip at random. State the probability of each outcome.

1. The number is less than 5.
2. The number ends in 5.
3. The number is even.
4. The number is divisible by 3.
5. The number is prime.
6. The digits have a sum of 10.
7. The number is less than 25.
8. The number contains a "1."

There are 5 purple marbles, 7 gold marbles, and 3 red marbles in a bag. Suppose one marble is chosen at random. Find each probability.

9. [tex]\(P\)[/tex] (gold)
10. [tex]\(P\)[/tex] (purple)
11. [tex]\(P\)[/tex] (red or gold)
12. [tex]\(P\)[/tex] (not red)

Standardized Test Practice:

What is the probability of rolling a number other than a 1 or 2 on a number cube?

A. [tex]\(\frac{5}{6}\)[/tex]
B. [tex]\(\frac{2}{3}\)[/tex]
C. [tex]\(\frac{1}{2}\)[/tex]
D. [tex]\(\frac{1}{3}\)[/tex]



Answer :

GinnyAnswer
Certainly, let's tackle each of these questions methodically:

### Probabilities with Slips of Paper (Numbers 1-20)
Consider the numbers from 1 to 20, written on slips of paper and placed in a bowl. The probability of drawing a slip at random that satisfies certain conditions can be calculated as follows:

#### 3. The number is less than 5.
The numbers less than 5 are [tex]\(1, 2, 3, \)[/tex] and [tex]\(4\)[/tex]. There are 4 such numbers.
[tex]\[ P(\text{number < 5}) = \frac{4}{20} = 0.2 \][/tex]

#### 4. The number ends in 5.
The number ending in 5 within the range of 1-20 is [tex]\(5\)[/tex] only. There is 1 such number.
[tex]\[ P(\text{number ends in 5}) = \frac{1}{20} = 0.05 \][/tex]

#### 5. The number is even.
The even numbers between 1 and 20 are [tex]\(2, 4, 6, 8, 10, 12, 14, 16, 18, \)[/tex] and [tex]\(20\)[/tex]. There are 10 such numbers.
[tex]\[ P(\text{number is even}) = \frac{10}{20} = 0.5 \][/tex]

#### 6. The number is divisible by 3.
The numbers divisible by 3 between 1 and 20 are [tex]\(3, 6, 9, 12, 15, \)[/tex] and [tex]\(18\)[/tex]. There are 6 such numbers.
[tex]\[ P(\text{number divisible by 3}) = \frac{6}{20} = 0.3 \][/tex]

#### 7. The number is prime.
The prime numbers between 1 and 20 are [tex]\(2, 3, 5, 7, 11, 13, 17, \)[/tex] and [tex]\(19\)[/tex]. There are 8 such numbers.
[tex]\[ P(\text{number is prime}) = \frac{8}{20} = 0.4 \][/tex]

#### 8. The digits have a sum of 10.
The numbers between 1 and 20 whose digits sum to 10 is [tex]\(19\)[/tex] only. There is 1 such number.
[tex]\[ P(\text{digits sum to 10}) = \frac{1}{20} = 0.05 \][/tex]

#### 9. The number is less than 25.
All numbers from 1 to 20 are less than 25. There are 20 such numbers.
[tex]\[ P(\text{number < 25}) = \frac{20}{20} = 1.0 \][/tex]

#### 10. The number contains a "1".
The numbers between 1 and 20 that contain a "1" are [tex]\(1, 10, 11, 12, 13, 14, 15, 16, 17, \)[/tex] and [tex]\(19\)[/tex]. There are 11 such numbers.
[tex]\[ P(\text{number contains a "1"}) = \frac{11}{20} = 0.55 \][/tex]

### Probabilities with Marbles (5 Purple, 7 Gold, 3 Red)
Now, consider the problem with marbles. The total number of marbles is [tex]\(5 + 7 + 3 = 15\)[/tex].

#### 11. [tex]\(P(\text{gold})\)[/tex]
There are 7 gold marbles.
[tex]\[ P(\text{gold}) = \frac{7}{15} \approx 0.4666666666666667 \][/tex]

#### 12. [tex]\(P(\text{purple})\)[/tex]
There are 5 purple marbles.
[tex]\[ P(\text{purple}) = \frac{5}{15} = \frac{1}{3} \approx 0.3333333333333333 \][/tex]

#### 13. [tex]\(P(\text{red or gold})\)[/tex]
The red and gold marbles together are [tex]\(3 + 7 = 10\)[/tex] marbles.
[tex]\[ P(\text{red or gold}) = \frac{10}{15} = \frac{2}{3} \approx 0.6666666666666666 \][/tex]

#### 14. [tex]\(P(\text{not red})\)[/tex]
The non-red marbles are the purple and gold marbles together [tex]\(5 + 7 = 12\)[/tex] marbles.
[tex]\[ P(\text{not red}) = \frac{12}{15} = 0.8 \][/tex]

### Rolling a Number Cube (Die)
A standard number cube, or die, has 6 faces numbered from 1 to 6.

#### 15. The probability of rolling a number other than a 1 or 2.
The favorable outcomes are rolling a 3, 4, 5, or 6. There are 4 such outcomes.
[tex]\[ P(\text{not 1 or 2}) = \frac{4}{6} = \frac{2}{3} \approx 0.6666666666666666 \][/tex]

Thus, for the standardized test practice, the correct answer is [tex]\( \mathbf{B\ \frac{2}{3}} \)[/tex].