Question

1. If one letter is chosen at random from the word combed, what is the probability that the letter chosen will be a "d"?

2. The sides of number cube have the numbers 2,4,8,9,4, and 7. If the cube is thrown once, what is the probability of rolling a 7?

3. A bag contains 12 red marbles, 10 green marbles, 2 yellow marbles, 19 blue marbles, and 9 purple marbles. What is the probability of pulling out a green marble?

Answer 1

1.) 1/6 Chance the letter will be D due to having 1 letter D out of 6 total leters
2.) 1/6 Chance of rolling a 7 due to having 6 total numbers and only one 7
3.) 10/52 Chance of pulling green due to only having 10 green marbles and 52 total marbles

Answer 2

• Probability that the chosen letter is d is
  `(1)/(6)`

• Probability of rolling a 7 is
  `(1)/(6)`
• Probability of picking a green is
  `(5)/(21)`

Explanation:

• Probability of choosing d in the word "combed"

Given:

Alphabet: d

Word: combed

First, we note down the length of the word "combed";

The length is 6 characters

The we check the number of occurrence of d in the word "combed"

Occurrence of d = 1

Probability is then calculated as;

Probability of choosing d =
`(Number of Occurrence)/(Total Observation)`

By Substitution; Probability =
`(1)/(6)`

• Probability of rolling a 7 in a cube of side numbers 2,4,8,9,4, and 7

Given:

Roll number = 7

Sample Space= {2,4,8,9,4, 7}

Sample Size, n(S) = 6

We check the number of occurrence of 7 in the sample space

Number of occurrence = 1

Probability is then calculated as;

Probability of rolling a 7 =
`(Number of Occurrence)/(Sample Size)`

By Substitution; Probability =
`(1)/(6)`

• Probability of pulling out a green marble

Given

Red = 12

Green = 10

Yellow = 2

Blue = 19

Purple = 9

Total = 12 + 10 + 2 + 19 + 9 = 42

Probability of picking a green marble is then calculated as;

Probability of choosing d =
`(Number of Green)/(Total)`

By Substitution; Probability =
`(10)/(42)`

Probability =
`(5)/(21)`