You roll a number cube twice. Find P (even, then not 2). Write the probabilty as a fraction in simplest form.
The possible outcomes for rolling a number cube twice are:
1-1, 1-2, 1-3, 1-4, 1-5, 1-6
2-1, 2-2, 2-3, 2-4, 2-5, 2-6
3-1, 3-2, 3-3, 3-4, 3-5, 3-6
4-1, 4-2, 4-3, 4-4, 4-5, 4-6
5-1, 5-2, 5-3, 5-4, 5-5, 5-6
6-1, 6-2, 6-3, 6-4, 6-5, 6-6
Out of these 36 possible outcomes, the even numbers are: 2, 4, 6.
The outcomes that are even and not 2 are: 4, 6.
So, the probability of rolling an even number on the first roll and a number that is not 2 on the second roll is:
P(even, then not 2) = 2/36 = 1/18.
Therefore, the probability is 1/18.
To find the probability of rolling an even number and then not rolling a 2 on a number cube, we need to calculate the number of favorable outcomes and the total number of possible outcomes.
1. For the first roll:
- The probability of rolling an even number is 3 out of 6, since there are three even numbers on a standard number cube (2, 4, and 6).
- The remaining outcomes on the first roll, which are not 2, are 5 out of 6, since there are six possible outcomes on a number cube.
2. For the second roll:
- The probability of not rolling a 2 on the second roll remains the same, which is 5 out of 6, since we are considering all the outcomes except for 2.
To find the probability of both events happening, we multiply the probabilities together:
Probability (even, then not 2) = (3/6) x (5/6)
Simplifying the fraction, we get:
Probability (even, then not 2) = 15/36
So, the probability of rolling an even number and then not rolling a 2 on a number cube is 15/36.