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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.
a. Predict how many students practice every day.
b. What is the sample size?
a. To predict how many students practice every day, we can set up a proportion:
7/12 = x/144
Solving for x, we get:
x = (7/12) * 144
x ≈ 84
Therefore, we can predict that approximately 84 martial arts students practice every day.
b. The sample size is the number of students in the study, which is given as 144. Therefore, the sample size is 144.
You roll a number cube twice. Find P(even, then not 2). Write the probability as a fraction in simplest form.
The number cube has six equally likely outcomes: 1, 2, 3, 4, 5, or 6, with a probability of 1/6 for each outcome.
The probability of rolling an even number on the first roll is 3/6 or 1/2 (since there are three even numbers: 2, 4, and 6, out of six possible outcomes).
If an even number is rolled on the first roll, then there are five possible outcomes left, and only one of them is a 2. Therefore, the probability of rolling an even number on the first roll and not rolling a 2 on the second roll is:
P(even, then not 2) = P(even) x P(not 2 | even)
P(even, then not 2) = (1/2) x (4/5) (since there are 4 options out of 5 that are not 2)
P(even, then not 2) = 2/5
Therefore, the probability of rolling an even number on the first roll and not rolling a 2 on the second roll is 2/5 or 0.4 as a decimal.
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, since there is one favorable outcome (rolling a 3) out of six possible outcomes (rolling a 1, 2, 3, 4, 5, or 6). Therefore, the theoretical probability of rolling a 3 can be written as the fraction 1/6 in simplest form.
b. The experimental probability of rolling a 3 is found by dividing the number of times a 3 came up (67) by the total number of rolls (450). So,
Experimental probability of rolling a 3 = Number of times a 3 came up/Total number of rolls
Experimental probability of rolling a 3 = 67/450
We can simplify this fraction by dividing both the numerator and denominator by the greatest common factor (GCF), which is 1:
Experimental probability of rolling a 3 = 67/450 (in simplest form)
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
There are a total of 12 letters, and only 2 of them are A's. Therefore, the probability of drawing an A is:
a. P(A) = 2/12
This fraction can be further simplified by dividing both the numerator and denominator by their greatest common factor (which is 2 in this case):
P(A) = 1/6 (in simplest form)
b. As a decimal, P(A) is 0.1667 (rounded to four decimal places)
c. As a percent, P(A) is 16.67% (rounded to two decimal places)