There are four different possible hair colours: red, brunette, brown and blonde. Assume that each haircolour is equally likely. If there are 5 people in a room, what is the probability that at least 2 have the same coloured hair?
1
since there are only 4 colors and 5 people, two people must have the same hair color!
I don't think that's how it works
To find the probability that at least two people have the same colored hair among the five people in the room, we can calculate the probability by finding the complement of the event where all five people have different hair colors.
First, let's calculate the probability that all five people have different hair colors:
For the first person, any hair color can be chosen, so the probability is 1.
For the second person, there are only 3 remaining hair colors to choose from (excluding the one chosen for the first person), so the probability is 3/4.
For the third person, there are 2 remaining hair colors to choose from, so the probability is 2/4 = 1/2.
For the fourth person, there is 1 remaining hair color to choose from, so the probability is 1/4.
For the fifth person, there is only 1 remaining hair color left, so the probability is 1/4.
Now, we multiply all these probabilities together to find the probability that all five people have different hair colors:
P(All different) = 1 * (3/4) * (1/2) * (1/4) * (1/4) = 3/128
Finally, we can find the probability that at least two people have the same hair color by subtracting the probability of all different hair colors from 1 (since the complementary events add up to 1):
P(at least 2 same) = 1 - P(All different) = 1 - 3/128 = 125/128
Therefore, the probability that at least two people have the same hair color among the five people in the room is 125/128.