Marissa is researching information about martial arts students. She found that 7 out of 12 martial artists practice every day. There are 144 martial arts students at a school.

Question

a. Predict how many students practice every day.

b. What is the sample size?

Answer 1

a. To find the number of students who practice every day, we can set up a proportion:

7/12 = x/144

where x is the number of students who practice every day.

To solve for x, we can cross-multiply:

12x = 7 * 144

x = (7 * 144) / 12

x = 84

Therefore, we can predict that 84 students practice every day.

b. The sample size is the total number of martial arts students at the school, which is given to be 144.

Answer 2

You roll a number cube twice. Find P(even, then not 2). Write the probability as a fraction in simplest form.

Answer 3

There are six possible outcomes when you roll a number cube: 1, 2, 3, 4, 5, or 6. Out of these, three are even: 2, 4, and 6.

If we roll the number cube twice, there are 6 x 6 = 36 possible outcomes. To find the probability of rolling an even number first and then not rolling a 2, we can use the formula:

P(even, then not 2) = P(even) x P(not 2 | even)

The probability of rolling an even number first is 3/6 since three out of the six possible outcomes are even.

If we roll an even number first, there are five possible outcomes that are not 2: 1, 3, 4, 5, and 6. Out of these, four outcomes are equally likely and lead to our desired event. So the probability of not rolling a 2 given that we rolled an even number is 4/5.

Therefore:

P(even, then not 2) = (3/6) x (4/5)

P(even, then not 2) = (1/2) x (4/5)

P(even, then not 2) = 2/5

So the probability of rolling an even number first and then not rolling a 2 is 2/5.

Answer 4

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

Answer 5

There are 12 letters in the mix, with two of them being 'A'.

a. The probability of drawing an 'A' is the number of 'A's in the mix, divided by the total number of letters. So,

P(A) = number of A's / total number of letters
P(A) = 2 / 12

We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 2:

P(A) = 1 / 6

b. To convert this fraction to a decimal, we can divide 1 by 6:

P(A) = 1/6 = 0.166666... (rounded to six decimal places)

c. To convert the decimal to a percent, we can multiply by 100:

P(A) = 0.166666... x 100% = 16.666...% (rounded to three decimal places)

Therefore, the probability of drawing an 'A' is:

a. 1/6
b. 0.166666...
c. 16.666...%