Two eight-sided number cubes are thrown. Given that one of the cubes shows a five, what is the
probability that the sum of the numbers that come up on the two cubes is six?
Since 5 + 1 = 6, 1 is one of 8 choices on the second cube, 1/8.
To find the probability that the sum of the numbers is six, we need to determine the number of favorable outcomes and the total number of possible outcomes.
Let's break down the problem step by step:
Step 1: Determine the total number of possible outcomes.
Since we are throwing two eight-sided number cubes, each cube has 8 possible outcomes (numbers 1 through 8). Therefore, the total number of possible outcomes is 8 * 8 = 64.
Step 2: Determine the number of favorable outcomes.
Given that one of the cubes shows a five, we can consider two scenarios:
a) The first cube shows a five, and the second cube shows a one.
b) The first cube shows a one, and the second cube shows a five.
For scenario a), there is only one favorable outcome because there is only one possible combination where the first cube shows a five, and the second cube shows a one (5,1).
For scenario b), there is also only one favorable outcome because there is only one possible combination where the first cube shows a one, and the second cube shows a five (1,5).
Therefore, the total number of favorable outcomes is 1 + 1 = 2.
Step 3: Calculate the probability.
To calculate 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
In this case, the probability is: 2 / 64 = 1 / 32.
Therefore, the probability that the sum of the numbers is six, given that one cube shows a five, is 1/32.