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.
First, we need to find the probability of rolling an even number on the first roll. There are three even numbers: 2, 4, and 6. So the probability of rolling an even number on the first roll is 3/6, which can be simplified to 1/2.
Next, we need to find the probability of rolling a number that is not 2 on the second roll, given that the first roll was an even number. This means there are only two possible outcomes for the first roll: 2 or 4. If the first roll was a 2, then the only possible option for the second roll to satisfy the condition of "not 2" is 4. If the first roll was a 4, then there are four possible options for the second roll that satisfy the condition of "not 2": 1, 3, 4, or 5.
Therefore, the probability of rolling an even number on the first roll and then rolling a number that is not 2 on the second roll is:
(1/2) x [(1/6) + (4/6)] = (1/2) x (5/6) = 5/12
So, P(even, then not 2) = 5/12.
in one sentance answer the questions, You roll a number cube twice. Find P(even, then not 2). Write the probability as a fraction in simplest form.
The probability of rolling an even number on the first roll and then rolling a number that is not 2 on the second roll 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 on a number cube is 1/6. This is because there is one face with a 3 out of six total faces.
b. The experimental probability of rolling a 3 is found by dividing the number of times a 3 came up by the total number of rolls:
Experimental probability = (number of times 3 came up) / (total number of rolls)
Experimental probability = 67/450
This fraction cannot be simplified anymore, so the experimental probability of rolling a 3 is 67/450.
To find the probability of rolling an even number first, and then rolling a number that is not 2, we need to determine the number of favorable outcomes and the total number of possible outcomes.
Step 1: Determine the favorable outcomes
When rolling a number cube, there are 6 possible outcomes: 1, 2, 3, 4, 5, and 6. Out of these, half are even numbers: 2, 4, and 6. So, the favorable outcomes for rolling an even number first are 3.
Step 2: Determine the total possible outcomes
Since you are rolling the number cube twice, the total possible outcomes for each roll are 6. Therefore, the total possible outcomes for two rolls are 6 x 6 = 36.
Step 3: Calculate the probability
To calculate the probability of rolling an even number first, and then not rolling a 2, we need to multiply the probabilities of each event.
The probability of rolling an even number first is 3/6, which simplifies to 1/2. (Three favorable outcomes out of six total possible outcomes.)
For the second roll, there are only 5 favorable outcomes (excluding the number 2, which we don't want). So, the probability of not rolling a 2 on the second roll is 5/6.
To find the probability of both events happening, we multiply the individual probabilities:
P(even, then not 2) = P(even) × P(not 2)
P(even, then not 2) = (1/2) × (5/6)
Multiplying the numerators: 1 × 5 = 5
Multiplying the denominators: 2 × 6 = 12
Therefore, P(even, then not 2) = 5/12.