If there are 6 red disks numbered 1 through 6, and 4 yellow disks numbered 7 through 10, find the probability of selecting a yellow disk given that the number selected is less than or equal to 4 or greater than or equal to 8.

10 disks

7 or 8 makes 2 possibilities

2/10 = 1/5

To find the probability of selecting a yellow disk given the given condition, we need to determine the number of favorable outcomes (selecting a yellow disk) and the number of total outcomes (selecting a red or yellow disk).

Let's break it down into two parts:
1. Selecting a yellow disk when the number selected is less than or equal to 4.
2. Selecting a yellow disk when the number selected is greater than or equal to 8.

Part 1: Selecting a yellow disk when the number selected is less than or equal to 4
In this case, we need to consider the red disks numbered 1, 2, 3, and 4.
Number of favorable outcomes (yellow disks): 0 (since there are no yellow disks numbered 1 to 4)
Number of total outcomes: 4 (the red disks numbered 1 to 4)

Part 2: Selecting a yellow disk when the number selected is greater than or equal to 8
In this case, we need to consider the yellow disks numbered 8, 9, and 10.
Number of favorable outcomes (yellow disks): 3 (the yellow disks numbered 8, 9, and 10)
Number of total outcomes: 7 (the red disks numbered 1 to 6 and the yellow disks numbered 7 to 10)

Now, let's calculate the probability of each part:
Part 1: Probability of selecting a yellow disk when the number selected is less than or equal to 4 is 0/4 = 0.
Part 2: Probability of selecting a yellow disk when the number selected is greater than or equal to 8 is 3/7.

To calculate the overall probability, we need to add the probabilities of each part since the two parts are mutually exclusive (they cannot occur at the same time). So, the overall probability is 0 + 3/7 = 3/7.

Therefore, the probability of selecting a yellow disk given that the number selected is less than or equal to 4 or greater than or equal to 8 is 3/7.

To find the probability of selecting a yellow disk given that the number selected is less than or equal to 4 or greater than or equal to 8, we need to determine the number of favorable outcomes and the number of possible outcomes.

First, let's calculate the number of favorable outcomes, i.e., the number of ways to select a yellow disk given the specified conditions.

- When the number selected is less than or equal to 4, there are no yellow disks available. Therefore, there are 0 favorable outcomes in this case.

- When the number selected is greater than or equal to 8, we can select any of the 4 yellow disks (numbered 7 through 10). Therefore, there are 4 favorable outcomes in this case.

Next, let's calculate the number of possible outcomes, i.e., the total number of ways we can select a disk from the given set.

- If the number selected is less than or equal to 4 or greater than or equal to 8, the possible outcomes would be all the disks available in the set. In this case, we have a total of 6 red disks and 4 yellow disks, so the number of possible outcomes is 10.

Now we can calculate the probability using the formula: probability = favorable outcomes / possible outcomes.

Probability of selecting a yellow disk given that the number selected is less than or equal to 4 or greater than or equal to 8 = (number of favorable outcomes) / (number of possible outcomes)
= 4 / 10
= 2 / 5

Therefore, the probability of selecting a yellow disk given that the number selected is less than or equal to 4 or greater than or equal to 8 is 2/5 or 0.4.