Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. You roll a number cube twice. Find P(even, then not 2). Write the probability as a fraction in simplest form.
There are six possible outcomes when rolling a number cube: 1, 2, 3, 4, 5, or 6.
For the first roll, there are three even numbers: 2, 4, and 6. Therefore, the probability of rolling an even number on the first roll is 3/6 or 1/2.
However, we want the probability of rolling an even number first AND NOT rolling a 2 on the second roll.
If we roll an even number first, there are five possible outcomes for the second roll (we can't roll a 2 again): 1, 3, 4, 5, or 6.
Therefore, the probability of rolling an even number first and NOT rolling a 2 on the second roll is:
1/2 * 5/6 = 5/12
So, P(even, then not 2) is 5/12.
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 is the number of ways to get a 3 divided by the total number of possible outcomes. Since there is only one way to get a 3, and there are a total of six possible outcomes, the theoretical probability is:
1/6
b. The experimental probability of rolling a 3 is the number of times a 3 comes up divided by the total number of rolls. From the problem, we know that 3 came up 67 times out of 450 rolls. So:
67/450
Both probabilities cannot be simplified any further.
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
There are a total of 12 letters, and only two of them are A's. Therefore, the probability of drawing an A is:
a. 2/12, which simplifies to 1/6
b. 1/6 is equivalent to 0.16666666667 when rounded to 11 decimal places.
c. To convert the decimal to a percent, we multiply by 100:
0.16666666667 x 100% = 16.666666667%, which when rounded to 2 decimal places is 16.67%.
Therefore, P(A) = 1/6 = 0.16666666667 = 16.67%.