If x,y can take values from the set (1,2,3,4),find the probability that the product of x and y is not greater than 6?
how many products xy are there? Just list them:
1,2,3,4,2,4,6,8,...
How many unique products are there? (delete duplicates)
how many xy <= 6?
Now just divide to find the probability.
To find the probability that the product of x and y is not greater than 6, we need to determine the number of favorable outcomes (the pairs of numbers whose product is less than or equal to 6) and the total number of possible outcomes.
Let's analyze the possible values of x and y:
1. If x = 1, then y can take the values 1, 2, 3, or 4.
2. If x = 2, then y can take the values 1, 2, 3, or 4.
3. If x = 3, then y can take the values 1, 2, or 3.
4. If x = 4, then y can only take the value 1.
Now, let's calculate the favorable outcomes:
For x = 1, the favorable outcomes are:
- (1, 1),
- (1, 2),
- (1, 3),
- (1, 4).
For x = 2, the favorable outcomes are:
- (2, 1),
- (2, 2),
- (2, 3),
- (2, 4).
For x = 3, the favorable outcomes are:
- (3, 1),
- (3, 2),
- (3, 3).
For x = 4, the favorable outcome is:
- (4, 1).
The total number of favorable outcomes is 14.
Now, let's calculate the total number of possible outcomes:
Since x and y can take values from the set (1, 2, 3, 4), there are a total of 4 possibilities for both x and y. Therefore, the total number of possible outcomes is 4 * 4 = 16.
To find the probability, we divide the number of favorable outcomes by the total number of possible outcomes:
Probability = Favorable outcomes / Total outcomes = 14 / 16 = 7 / 8.
So, the probability that the product of x and y is not greater than 6 is 7/8.