Probability Distributions

Question

In a box of smarties there are eight different colours which normally occur in equal proportions. Rachael is given 24 smarties, and orange ones are her favourite. Assume they come from a very large box.

(i) How many orange ones would she expect to get?

(ii) What is the probability that she gets this number?

(iii) What is the probability that she gets fewer orange ones?

(iv) What is the probability that she gets more orange ones than she expected?

I have done the first 3 parts of the question. I only need to do the last one.

Answer 1

Nice job working through most of this problem, Emma! The last part will be pretty easy, since you have parts ii and iii done. There are three possible outcomes: she gets fewer orange than expected, she gets exactly the number expected, or she gets more than expected. Together these probabilities should sum to 1 (i.e. 100% of the time, one of those three things happen because those are the only possibilities).

So to find the answer to part iv:

P(more than expected) = 1 - P(less than expected) - P(exactly as many as expected)

I hope this explanation helps you!