The theoretical probability of a simple event is P(event) = number of favorable outcomestotal number of outcomes in a sample space EXAMPLE: A jar contains 10 green, 7 red, and 3 blue marbles. What is the probability of randomly picking a red marble? P(red) = number of red marblestotal number of marbles in the sample space=710+7+3=720 The probability of randomly picking a red marble is 720=0.35=35% Use the spinner below to complete the problem. Determine the probability of the spinner landing on a 3.(3 points)Enter the probability as a SIMPLIFIED fraction: Enter the probability as a decimal with two decimal places: Enter the probability as a percent: %
To determine the probability of the spinner landing on a 3, we first need to identify the total number of possible outcomes on the spinner.
Since a spinner typically has 8 equal sections, the total number of outcomes in the sample space is 8.
Next, we need to determine the number of favorable outcomes, which in this case is the number of sections labeled as 3. Since there is only 1 section labeled as 3, the number of favorable outcomes is 1.
Therefore, the probability of the spinner landing on a 3 is:
Simplified fraction: 1/8
Decimal: 0.125
Percent: 12.5%
Caleb is creating a sign with the words
T H E U N I T E D S T A T E S O F A M E R I C A
with each letter having its own cutout. If a letter is randomly chosen, complete each part below.
(3 points)
Part 1. What is the probability Caleb will choose the letter A?
Enter the probability as a decimal rounded to the thousandth place. (3 digits)
In the phrase "THE UNITED STATES OF AMERICA" there are a total of 24 letters.
There are a total of 2 letter As in the phrase: one in "STATES" and one in "AMERICA".
Therefore, the probability of Caleb choosing the letter A is:
Number of favorable outcomes (choosing the letter A) = 2
Total number of outcomes = 24
Probability = 2/24 = 1/12 ≈ 0.083
So, the probability of choosing the letter A is 0.083.
Part 2. What is the probability Caleb will choose a consonant?
Enter the probability as a decimal rounded to the thousandth place. (3 digits)
To calculate the probability of choosing a consonant from the phrase "THE UNITED STATES OF AMERICA", we first need to determine the total number of letters in the phrase that are consonants.
There are 13 consonants in the phrase: T, H, N, T, D, S, T, S, F, M, R, C, and M.
Since there are a total of 24 letters in the phrase, the probability of Caleb choosing a consonant is:
Number of favorable outcomes (choosing a consonant) = 13
Total number of outcomes = 24
Probability = 13/24 ≈ 0.542
Therefore, the probability of Caleb choosing a consonant is approximately 0.542.
Part 3. What is the probability Caleb will choose a letter from the word “of”?
Enter the probability as a decimal rounded to the thousandth place. (3 digits)
In the word "of", there are a total of 2 letters. The letter "o" appears twice in the word.
To calculate the probability of choosing a letter from the word "of" from the phrase "THE UNITED STATES OF AMERICA", we first need to determine the total number of letters in the phrase that are from the word "of".
There are 2 letters from the word "of" in the phrase: one "o" and one "f".
Since there are a total of 24 letters in the phrase, the probability of Caleb choosing a letter from the word "of" is:
Number of favorable outcomes (choosing a letter from the word "of") = 2
Total number of outcomes = 24
Probability = 2/24 = 1/12 ≈ 0.083
Therefore, the probability of Caleb choosing a letter from the word "of" is approximately 0.083.