This was originally posted on another student's thread.
Hey can I have some help here?
My question:
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.
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posted by Chloe
today at 4:20pm
half the faces are odd, and half are even
one face is 2 , so five (out of six) are not
the two rolls are separate, independent events
... this means multiply the individual probabilities
To find the probability of rolling an even number followed by a number that is not 2, we need to consider the possible outcomes and their probabilities.
First, let's determine the total number of outcomes when rolling a number cube twice. Since each roll has 6 possible outcomes (numbers from 1 to 6), the total number of outcomes for two rolls is 6x6 = 36.
Next, let's determine the number of favorable outcomes, i.e., the outcomes where we roll an even number followed by a number that is not 2.
For the first roll, the favorable outcomes are 2, 4, and 6 because they are the even numbers. After that, for the second roll, any number excluding 2 (1, 3, 4, 5, 6) will be a favorable outcome.
Therefore, the number of favorable outcomes is 3 (even numbers) x 5 (numbers excluding 2) = 15.
Lastly, we can find the probability by dividing the number of favorable outcomes (15) by the total number of outcomes (36). So, the probability of rolling an even number followed by a number that is not 2 is 15/36.
To simplify the fraction 15/36, you can divide both the numerator and denominator by their greatest common divisor, which is 3 in this case. Cancelling out the common factor, we get 15/36 = 5/12.
So, the probability is 5/12.