The numbers 1 through 9 are written on slips of paper and placed into a hat. Two slips are randomly drawn. If the first slip of paper is not returned to the hat after it is drawn, find the probability of getting a six and then a three?
To find the probability of getting a six and then a three, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Step 1: Determine the total number of outcomes:
When two slips are drawn from a hat without replacement, the total number of outcomes can be calculated using the formula "nPr" (permutation).
The number of ways to arrange (permutations) two slips out of nine is given by:
9P2 = 9! / (9 - 2)!
= 9! / 7!
= (9 * 8) / (2 * 1)
= 72
So, there are 72 possible outcomes when two slips are drawn from the hat without replacement.
Step 2: Determine the number of favorable outcomes:
Since we want to find the probability of getting a six and then a three, we need to determine the number of ways to choose these slips.
The number of ways to choose a six and then a three is 1 (as there is only one slip with a six and one slip with a three in the hat).
Step 3: Calculate the probability:
The probability can be calculated by dividing the number of favorable outcomes by the total number of outcomes.
Probability = Number of favorable outcomes / Total number of outcomes
= 1 / 72
= 0.0139 (rounded to four decimal places)
Therefore, the probability of getting a six and then a three is approximately 0.0139 or 1.39%.
To find the probability of getting a six and then a three, we first need to determine the number of possible outcomes and the number of favorable outcomes.
There are nine slips of paper in the hat, and two are randomly drawn without replacement. The number of possible outcomes can be calculated using combinations. We can use the formula for combinations, which is nCr = n! / (r! * (n - r)!), where n is the total number of items and r is the number of items being chosen.
In this case, there are 9 slips of paper, so n = 9. We are choosing 2 slips, so r = 2. Therefore, the number of possible outcomes can be calculated as:
9C2 = 9! / (2! * (9 - 2)!)
= 9! / (2! * 7!)
= (9 * 8 * 7!) / (2! * 7!)
= (9 * 8) / 2
= 36
So, there are 36 possible outcomes when drawing two slips of paper from the hat without replacement.
Now, let's determine the number of favorable outcomes. We want to get a six and then a three. Since we are not returning the first slip to the hat, we have one less slip to choose from for the second slip. The number of favorable outcomes can be calculated as:
1C1 * 1C1 = 1 * 1 = 1
Therefore, there is 1 favorable outcome of getting a six and then a three.
Now we can calculate the probability by dividing the number of favorable outcomes by the number of possible outcomes:
Probability = Number of Favorable Outcomes / Number of Possible Outcomes
Probability = 1/36
So, the probability of getting a six and then a three is 1/36.