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.
The number cube has 6 sides, so it can produce 6 possible outcomes on each roll. To find the probability of rolling an even number followed by a number that is not 2, we need to first determine how many of the possible outcomes satisfy those conditions.
1. There are three even numbers on the cube: 2, 4, and 6.
2. There are two numbers that are not 2: 1, 3, 4, 5, and 6.
To calculate the probability of rolling an even number followed by a number that is not 2, we need to multiply the probabilities of each individual event.
P(even, then not 2) = P(even) x P(not 2|even)
P(even) = 3/6 = 1/2 (since there are 3 even numbers out of 6 possible outcomes)
P(not 2|even) = 4/5 (since there are 4 possible outcomes that are not 2 out of a total of 5 remaining outcomes after rolling an even number)
P(even, then not 2) = (1/2) x (4/5) = 2/5
Therefore, the probability of rolling an even number followed by a number that is not 2 is 2/5 in simplest form.
To find the probability of rolling an even number first and then not rolling a 2, we need to determine the number of favorable outcomes and the total number of possible outcomes.
Step 1: Determine the number of favorable outcomes (even, then not 2).
An even number can be rolled on a number cube in three ways: 2, 4, or 6. However, we don't want to roll a 2 on the second roll, so only the numbers 4 and 6 are favorable for the second roll. Thus, there are 2 favorable outcomes.
Step 2: Determine the total number of outcomes.
Since we are rolling a number cube twice, there are a total of 6 possible outcomes on the first roll and 6 possible outcomes on the second roll. Therefore, the total number of outcomes is 6 * 6 = 36.
Step 3: Calculate the probability as a fraction.
The probability of rolling an even number first and then not rolling a 2 is the ratio of the number of favorable outcomes to the total number of outcomes. So, the probability is 2/36.
Step 4: Simplify the fraction.
Both 2 and 36 can be divided by 2, so the fraction simplifies to 1/18.
Therefore, the probability of rolling an even number first and then not rolling a 2 is 1/18.