A ice cream shop sells 4 flavors of ice cream, assume that all orders of two scoops are equally likely, what is the probability that in an order of two scoops both are of the same flavor?
There are 4^2 ways of taking two scoops
Of those, only 4 are both the same
So, 4/16 = .25 is the chance that two random scoops are the same.
Or, you can consider it like this.
Given a first scoop of any flavor, there is a 25% chance that the 2nd scoop is the same, since there are 4 flavors.
To find the probability that in an order of two scoops both are of the same flavor, we first need to determine the total number of possible combinations of two scoops of ice cream from the four available flavors.
Since we are not concerned with the specific flavors, but only whether they are the same or different, we can calculate this by using combinations. The formula for combinations is nCr = n! / (r! * (n-r)!), where n is the total number of items and r is the number of items selected.
In this case, we have 4 flavors to choose from and we are selecting 2 scoops. So, we can calculate the total number of combinations as 4C2 = 4! / (2! * (4-2)!) = 4! / (2! * 2!) = 6.
Since all orders of two scoops are equally likely, each of these 6 combinations has the same probability of occurring.
Now, we need to determine the number of combinations where both scoops are of the same flavor. Since there are 4 flavors, each flavor can be chosen in 1 way, and we have 4 flavors to choose from. So, there are 4 combinations where both scoops are of the same flavor.
Therefore, the probability that in an order of two scoops both are of the same flavor is 4/6, which simplifies to 2/3, or approximately 0.667.