Numbered disks are placed in a box and one disk is selected at random. If there are 6 red disks numbered 1through 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 3 or greater than or equal to 8.
there are 3 discs ≤ 3
there are 3 discs ≥ 8
3 of these 6 discs are yellow, so P(yellow) = 3/6
To find the probability of selecting a yellow disk, given that the number selected is less than or equal to 3 or greater than or equal to 8, we need to determine the total number of favorable outcomes and the total number of possible outcomes.
First, let's identify the favorable outcomes:
- We have 4 yellow disks numbered 7 through 10.
- Out of these 4 yellow disks, the disks numbered 8, 9, and 10 satisfy the given condition (greater than or equal to 8).
So, we have 3 favorable outcomes.
Next, let's find the total number of possible outcomes:
- There are 6 red disks numbered 1 through 6.
- We also have 4 yellow disks numbered 7 through 10.
So, we have a total of 10 disks.
Therefore, the probability of selecting a yellow disk, given that the number selected is less than or equal to 3 or greater than or equal to 8 is:
Probability = (Number of favorable outcomes) / (Number of possible outcomes)
= 3 / 10
= 0.3
Hence, the probability of selecting a yellow disk, given the specified conditions, is 0.3 or 30%.
To find the probability of selecting a yellow disk given the conditions mentioned, we need to calculate the number of favorable outcomes and divide it by the total number of possible outcomes.
Step 1: Determine the favorable outcomes
The conditions state that we need to select a yellow disk given that the number is less than or equal to 3 or greater than or equal to 8.
Favorable outcomes:
- Yellow disks numbered 1, 2, 3
- Yellow disks numbered 8, 9, 10
So, the total number of favorable outcomes is 6 (3 yellow disks with numbers 1, 2, 3 and 3 yellow disks with numbers 8, 9, 10).
Step 2: Determine the total number of possible outcomes
The total number of possible outcomes is the total number of disks available in the box, which is the sum of the number of red disks and yellow disks.
Total number of possible outcomes = 6 (red disks) + 4 (yellow disks) = 10
Step 3: Calculate the probability
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 6 (number of favorable outcomes) / 10 (total number of possible outcomes)
Simplifying, we get:
Probability = 3/5
Therefore, the probability of selecting a yellow disk, given that the number selected is less than or equal to 3 or greater than or equal to 8, is 3/5 or 0.6.