Question

A vending machine offers 8 different drinks. One day, 6 employees each purchased a drink from the vending machine. Find the probability that at least 2 employees purchased the same drink. Round your answer to the nearest hundredth.

Answer 1

this is hard

Answer 2

I'm bad with stuff like this.

Answer 3

1-6/8

Answer 4

do you have the answer?

Answer 5

total cases:
each man has 8 choices.so total cases = 8^6.
each has different drink:
cases = 8*7*6*5*4*3.

for at least two have same drink = total cases - when each have different drink = 8^6 - 8*7*6*5*4*3.

probability = (8^6 - 8*7*6*5*4*3) / (8^6).

Answer 6

Okay, I got it:
First, you have a probability of getting 1 type of drink on a vending machine with 8 drinks:
\[P (Drink 1) = (1\div8)\]
but since the even requires at least 2 of the 6 employees to choose the same drink, we have:
\[P(Drink 1) = (1\div8) \times (6 employees \div 2 chosesamedrink)\]
\[P(1) = (1\div8)\times(6\div2)\]

Hope that helps, all you have to do now is to work from the right, divide 6 to two, and multiply it by 1/8. (Then simplify).

Answer 7

ok i finally got it thanks !!!

Answer 8

The first guy drinks a drink. It can be anything.
The second guy has a (7/8) chance of drinking something else. Now 2 different drinks have been drank.
The third guy has a (6/8) chance of drinking something else.
Fourth guy: (5/8)
fifth guy: (4/8)
sixth: (3/8)

Probability they all drink something different:
1*(7/8)*(6/8)*(5/8)*(4/8)*(3/8)

Answer 9

The probability that at least two drink the same thing will be
1-(that probability^)

Answer 10

smooth got it, go with that
also remember that "at least two" or "at least one" is a set up for "not one" or "not two"

Answer 11

But realistically, that's not a very good model of the probability. It assumes equally likely choices, and coke is way more popular than anything else.

Answer 12

coke adds life