Probability: Picking M&M's
I am a student in an Intro. Stat. class at a local community college.
I recently got a quiz back in which the teacher marked me wrong and upon questioning with more explicit detail he still told me I was wrong.
1) The Masterfoods company manufactures bags of Peanuts Butter M&M's. They report that they make 10% each brown and red candies, and 20% each yellow, blue, and orange candies. The rest of the candies are green.
--the last question on the quiz--
c. After picking 10 M&M's in a row, you still have not picked a red one. A friend says that you should have a better chance of getting a red candy on your next pick since you have yet to see one. Comment on your friends statement.
I answered that the friend is correct that in ideal circumstances probability has increased. (ideal, such as you didn't receive a bag with 0 red M&M's) This is covered by the friends diction of "should" any how.
The teacher said the correct answer is: Your friend is speaking nonsense.
P(picking a red) = N(number of red M&M's) / D(total number of M&M's)
or simplified to P = N/D.
After you have drawn out 10 M&M's previously the equation can be understood as P = N / (D-10)
It will not matter that you don't know what N or D is because you know that N has not changed but that the denominator has, no matter how many M&M's are in the bag the probability will increase. Substitute any non-zero number for the variables and the probability will increase.
If that is true then the friend is correct in assuming that you have a better chance of picking a red M&M.
This seems blatantly obvious to me. When I pressed my teacher he said "But you don't know the denominator" and I told him "that doesn't matter" and his response was "You are thinking to hard."
So, who is right? Me or the teacher?