Question

there are 400 jellybeans in a bag. 40 of them are blue. the rest are orange. what is the likelyhood of picking at least one blue jellybean when you pick 60 at random.

Answer 1

Think of the problem this way. When you see "at least one ..." , think of the complementary probability of 1 - "no blue jelly beans". That's the starting point.

Answer 2

So you would start with picking a jellybean and try to find the probability of "no blues". So, the first pick would be 360/400. That has to happen with the second one also not being blue, so you would be left with 399 jellybeans from which to pick of which you only have 359 orange ones left, so your second factor would be 359/399, so you would have two events necessary so far for a factor of 360/400 x 359/399. You have to carry this process out 60 times with decreasing numbers of jellybeans left and decreasing number of oranges left. This will be the probability of "no blues". Then, at the end, you subtact this number from 1. If you want, I could show you how to use factorial notation.

Answer 3

For your numerator, 360 x 359 x 358 x ... x 303 x 302 x 301 = 360! / 300! Any number N! means N x (N-1) x (N-2) x ... x 3 x 2 x 1. Are you with me so far?

Answer 4

yeah

Answer 5

So, do you see how I got the numerator? If you do, then you go through a similar process for the denominator.

Answer 6

yes thank you :)

Answer 7

If you like, you can show me the rest of your work on this and I can tell you if you are staying on the right track. If I don't hear back from you, then good luck and I hope you follow the rest of the steps well.

Answer 8

By the way, whoever gave you this problem is probably not expecting just a single number answer though I have no way of knowing that for sure. He is probably looking for an answer in the format of a formula with "!" notation. Are you still getting all this? It's a little harder than it looks at first.