i need help with this:

A friend and i go to a chinese restaurant every firday. our 2 fortune cookies list 6 #s between 1-55. we chack each week which ones match. If the numbers are truely random, calculate the possiblity of 0,1,2 ect. matching #s
There's a chart
outcomes(# matching #s)1 2 3 4 5 6
Probability ? ? ? ? ? ?

the probabilities must eqaul to 1

ktuuu

To calculate the possibilities of matching a certain number of numbers between the two sets of fortune cookie numbers, we can use the concept of combinations.

First, let's determine the total number of possible combinations. Since there are 55 possible numbers and 6 numbers being drawn, the total number of combinations is given by:

Total Combinations = Number of combinations of 6 numbers out of 55

Using the formula for combinations, this is calculated as:

Total Combinations = C(55, 6) = 55! / (6! * (55-6)!)

Next, let's calculate the probabilities for each outcome:

1. Probability of 0 matching numbers:
In this case, we need to choose 6 numbers from the remaining 49 numbers (since none of them can match). Therefore, the probability is given by:

P(0 matching numbers) = C(49, 6) / Total Combinations

2. Probability of 1 matching number:
Here, we need to choose 1 number that matches and 5 numbers that don't match. The probability can be calculated as:

P(1 matching number) = (C(6,1) * C(49,5)) / Total Combinations

3. Probability of 2 matching numbers:
Similarly, for 2 matching numbers, the probability is:

P(2 matching numbers) = (C(6,2) * C(49,4)) / Total Combinations

4. Probability of 3 matching numbers:

P(3 matching numbers) = (C(6,3) * C(49,3)) / Total Combinations

5. Probability of 4 matching numbers:

P(4 matching numbers) = (C(6,4) * C(49,2)) / Total Combinations

6. Probability of 5 matching numbers:

P(5 matching numbers) = (C(6,5) * C(49,1)) / Total Combinations

Note that the probability of having all 6 numbers matching is simply the probability of choosing those 6 specific numbers out of the 55 possible numbers:

P(6 matching numbers) = C(6,6) / Total Combinations

You can use these formulas to calculate the probabilities for each outcome. Remember, the sum of all the probabilities should equal 1.