Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
You mix the letters M, A, T, H, E, M, A, T, I, C, A, and L thoroughly. Without looking, you draw one letter. Find the probability P(A). Write the probability as:
a. a fraction in simplest form
b. a decimal
c. a percent
a. There are 12 letters total and 3 of them are A's. The fraction in simplest form is 3/12, which reduces to 1/4.
b. To find the decimal, divide 1 by 4: 1 ÷ 4 = 0.25.
c. To find the percent, multiply the decimal by 100: 0.25 × 100 = 25%.
Therefore, the probability of drawing an A is:
a. 1/4
b. 0.25
c. 25%
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
You mix the letters M, A, T, H, E, M, A, T, I, C, A, and L thoroughly. Without looking, you draw one letter. Find the probability P(A). Write the probability as:
a. a fraction in simplest form
b. a decimal
c. a percent
a. There are 12 letters total and 3 of them are A's. The fraction in simplest form is 3/12, which reduces to 1/4.
b. To find the decimal, divide 1 by 4: 1 ÷ 4 = 0.25.
c. To find the percent, multiply the decimal by 100: 0.25 × 100 = 25%.
Therefore, the probability of drawing an A is:
a. 1/4
b. 0.25
c. 25%
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
A number cube is rolled 450 times. The number 3 comes up 67 times.
a. What is the theoretical probability of rolling a 3? Write your answer as a fraction in simplest form.
b. What is the experimental probability of rolling a 3? Write your answer as a fraction in simplest form.
a. The theoretical probability of rolling a 3 on a number cube is 1/6. This is because there are 6 possible outcomes (numbers 1 through 6) and only one of them is a 3. Therefore, the theoretical probability of rolling a 3 is 1/6.
b. The experimental probability of rolling a 3 is found by dividing the number of times the 3 came up by the total number of rolls:
Experimental probability of rolling a 3 = 67/450
This fraction cannot be simplified further.
To find the probability of drawing the letter "A" from the letters M, A, T, H, E, M, A, T, I, C, A, and L, we need to determine the number of favorable outcomes (the number of A's) and the total number of possible outcomes (the total number of letters).
Step 1: Determine the number of A's.
The given set of letters contains 2 A's, so the number of favorable outcomes is 2.
Step 2: Determine the total number of letters.
The given set of letters contains 12 letters in total.
Step 3: Calculate the probability.
The probability (P) of drawing an A can be calculated as:
P(A) = favorable outcomes / total outcomes
a. P(A) as a fraction in simplest form:
P(A) = 2/12
= 1/6 (since both the numerator and denominator can be divided by 2)
b. P(A) as a decimal:
P(A) = 1/6
≈ 0.1667 (when rounded to four decimal places)
c. P(A) as a percent:
P(A) = 1/6
≈ 0.1667
≈ 16.67% (when multiplied by 100 and rounded to two decimal places)
To find the probability of drawing the letter "A" from the given set of letters, we need to determine the number of ways we can draw an "A" and divide it by the total number of possible outcomes.
Step 1: Determine the number of ways to draw an "A"
Since there are two "A" letters in the given set, there are two ways to draw an "A".
Step 2: Determine the total number of possible outcomes
The total number of letters in the set is 12.
Step 3: Calculate the probability
We divide the number of ways to draw an "A" (2) by the total number of possible outcomes (12):
a. Fraction: 2/12 = 1/6 (This fraction cannot be simplified any further.)
b. Decimal: 2 / 12 ≈ 0.1667 (rounded to four decimal places)
c. Percent: 1/6 ≈ 16.67% (rounded to two decimal places)
Therefore, the probability of drawing the letter "A" is:
a. 1/6
b. 0.1667
c. 16.67%