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. P(A) = 3/12 = 1/4
b. P(A) = 0.25
c. P(A) = 25%
To find the probability P(A), we need to determine the number of favorable outcomes (the number of times the letter A can be drawn) and the total number of possible outcomes (the total number of letters that can be drawn).
First, let's count the number of times the letter A appears in the set of letters: M, A, T, H, E, M, A, T, I, C, A, and L. We see that there are three A's in the set.
Next, let's count the total number of letters in the set. Since each letter is unique, there are a total of 12 letters.
a. The probability P(A) as a fraction in simplest form is the number of favorable outcomes divided by the total number of possible outcomes. In this case, the number of favorable outcomes is 3 (the number of A's) and the total number of possible outcomes is 12. Therefore, P(A) is 3/12, which simplifies to 1/4.
b. To express the probability P(A) as a decimal, divide the number of favorable outcomes by the total number of possible outcomes. In this case, P(A) is 3/12, which is equal to 0.25.
c. To express the probability P(A) as a percent, multiply the decimal form by 100. In this case, P(A) is 0.25, which is equal to 25%.