You roll a number cube twice. Find P(even, then not 2). Write the probability as a fraction in simplest form.
Only need the math.
There are 6 possible outcomes for the first roll and 5 possible outcomes for the second roll.
Out of the 6 possible outcomes for the first roll, 3 are even (2, 4, 6).
If the first roll is even, then there are 5 possible outcomes for the second roll, but we want to exclude the outcome of rolling a 2. Therefore, there are 4 favorable outcomes.
So the probability of rolling an even number on the first roll and then not rolling a 2 on the second roll is:
3/6 * 4/5 = 2/5
Therefore, P(even, then not 2) = 2/5.
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, or one out of six possible outcomes. 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 a 3 came up in the experiment (67) by the total number of rolls (450):
67/450 = 0.149 or approximately 15/100
Therefore, the experimental probability of rolling a 3 is 15/100, which can be simplified to 3/20.
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 in total, and only 2 of them are A's. Therefore, the probability of drawing an A is 2/12, which simplifies to 1/6.
b. 1/6 as a decimal is approximately 0.1667 (rounded to four decimal places).
c. 1/6 as a percent is approximately 16.67%.
To find the probability of rolling an even number and then not rolling a 2 on a number cube, we need to find the number of favorable outcomes and the total number of possible outcomes.
There are 3 even numbers on a number cube: 2, 4, and 6. And there are 5 numbers that are not 2: 1, 3, 4, 5, and 6.
The number of favorable outcomes is the number of ways we can roll an even number and then a number that is not 2. Since there are 3 even numbers and 5 numbers that are not 2, the number of favorable outcomes is 3 × 5 = 15.
The total number of possible outcomes is the number of ways we can roll a number cube twice. Since each roll has 6 possible outcomes, the total number of possible outcomes is 6 × 6 = 36.
Therefore, the probability of rolling an even number and then not rolling a 2 is 15/36.
To find the probability of rolling an even number, then rolling a number that is not 2 on a number cube, we need to determine the number of favorable outcomes and the number of possible outcomes.
Step 1: Determine the number of possible outcomes:
When you roll a number cube, there are 6 possible outcomes since there are 6 sides on a number cube.
Step 2: Determine the number of favorable outcomes for the first event (rolling an even number):
Out of the 6 possible outcomes, there are 3 even numbers (2, 4, and 6).
Step 3: Determine the number of favorable outcomes for the second event (rolling a number that is not 2):
Since we have already rolled an even number, we can exclude the number 2 from the possible outcomes. Therefore, there are 5 possible outcomes for the second roll (1, 3, 4, 5, and 6), and 4 favorable outcomes (3, 4, 5, and 6).
Step 4: Calculate the probability:
To calculate the probability of both events occurring, we multiply the probabilities of each event together.
Thus, the probability of rolling an even number, then rolling a number that is not 2, is (3/6) * (4/5), which simplifies to 12/30.
Therefore, the probability is 12/30, and it can be further simplified to 2/5 in simplest form.