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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, and 6.
To find P(even, then not 2), we need to determine the number of outcomes that are even and not 2, and then divide that by the total number of possible outcomes when rolling the number cube twice.
First, let's determine the number of outcomes that are even and not 2.
Even numbers are 2, 4, and 6. Out of these three even numbers, only one is not 2, which is 4. Therefore, there is only one outcome that is even and not 2.
Next, we need to find the total number of possible outcomes when rolling the number cube twice. This can be determined by multiplying the number of outcomes for each roll. Since there are six possible outcomes for each roll, the total number of possible outcomes is 6 x 6 = 36.
Finally, we can find the probability of rolling an even number, then not 2, by dividing the number of outcomes that meet the requirements (1) by the total number of possible outcomes (36):
P(even, then not 2) = 1/36
Therefore, the probability of rolling an even number, then not 2, is 1/36.
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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.
To find the probability of rolling an even number first, then not rolling a 2 on a number cube, we need to determine the number of favorable outcomes and the total number of possible outcomes.
Number cube has 6 sides numbered from 1 to 6.
Step 1: Determine the favorable outcomes:
- Rolling an even number first: The even numbers on a number cube are 2, 4, and 6. So, the favorable outcomes for rolling an even number first are 3.
Step 2: Determine the total number of possible outcomes:
- When rolling a number cube twice, the total number of outcomes is given by multiplying the number of sides on the number cube each time. Since each roll has 6 possible outcomes, the total number of outcomes is 6 * 6 = 36.
Step 3: Calculate the probability:
- The probability is given by the ratio of favorable outcomes to the total number of outcomes. So, the probability P(even, then not 2) = favorable outcomes / total outcomes.
= 3 / 36
= 1 / 12
Therefore, the probability as a fraction in simplest form is 1/12.
To find the probability of rolling an even number on the first roll and not rolling a 2 on the second roll, we need to determine the possible outcomes that satisfy these conditions and divide that by the total number of possible outcomes.
Step 1: Determine the possible outcomes for each roll.
A standard number cube has 6 sides, numbered 1 through 6, with 3 even numbers (2, 4, 6) and 3 odd numbers (1, 3, 5). Therefore, the possible outcomes for the first roll are {2, 4, 6}, and the possible outcomes for the second roll (assuming the first roll was not 2) are {1, 3, 4, 5, 6}.
Step 2: Determine the total number of possible outcomes.
Since each roll has 6 possible outcomes, the total number of possible outcomes for rolling the number cube twice is 6 x 6 = 36.
Step 3: Determine the favorable outcomes.
To find the favorable outcomes, we need to find the number of outcomes where the first roll is even (2, 4, or 6) and the second roll is not 2. This can be represented as the set {2, 4, 6} x {1, 3, 4, 5, 6}, which gives us the following 15 possible outcomes:
{(2, 1), (2, 3), (2, 4), (2, 5), (2, 6), (4, 1), (4, 3), (4, 4), (4, 5), (4, 6), (6, 1), (6, 3), (6, 4), (6, 5), (6, 6)}.
(Note: (a, b) represents the outcome of the first roll being a and the second roll being b)
Step 4: Calculate the probability.
To find the probability, we divide the number of favorable outcomes by the total number of possible outcomes: 15 / 36 = 5 / 12.
Therefore, the probability of rolling an even number on the first roll and not rolling a 2 on the second roll is 5/12.