You roll a number cube twice. Find P (even, then not 2). Write the probability as a fraction in simplest form. I'm fully clueless to the answer to this question. Can someone please help me out? Thanks Very Much and need the answer A.S.A.P!
There are 36 possible outcomes. How many of these are even and not 2?
Well, of the 36 outcomes, half are even and half are odd. But you want even≠2, so throw out 1,1. That leaves just 17/36
Just to be sure, list all possible successes:
13 15
22 24 26
31 33 35
42 44 46
51 53 55
62 64 66
Looks like P(even≠2) = 17/36
To find the probability of rolling an even number and then not rolling a 2 on a number cube, we need to first determine the sample space and the favorable outcomes.
Step 1: Determine the sample space
When rolling a number cube twice, the sample space consists of all possible outcomes. Each roll has 6 possible outcomes because there are 6 faces on a number cube. Since we are rolling it twice, the total number of possible outcomes is 6 * 6 = 36.
Step 2: Determine the favorable outcomes
To roll an even number, we need to consider the numbers 2, 4, and 6. Therefore, there are 3 favorable outcomes for the first roll. After rolling an even number on the first roll, we want to avoid rolling a 2 on the second roll. So for the second roll, there are 5 favorable outcomes (1, 3, 4, 5, and 6) out of the 6 possible outcomes.
Step 3: Calculate the probability as a fraction in simplest form
To find the probability, we divide the number of favorable outcomes by the total number of possible outcomes.
Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
Probability = (3 * 5) / 36
Probability = 15/36
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 3.
Probability = 15/36 = 5/12
Therefore, the probability of rolling an even number and then not rolling a 2 on a number cube is 5/12.