Probability question (Textbook question that does not have an answer in the back)

Question

The Sorry State Lottery requires you to select five different numbers from 0 through 49. (Order is not important.) You are a Big Winner if the five numbers you select agree with those in the drawing, and you are a Small-Fry Winner if four of your five numbers agree with those in the drawing.What is the probability of being a Big Winner? What is the probability of being a Small-Fry Winner?What is the probability that you are either a Big Winner or a Small-Fry Winner?

Answer 1

You need the hypergeometric distribution to solve these, which is simply a proportion of the combinations of your sample (the 5 numbers you choose) and population (all 49 numbers available to be chosen).

 

 

P(all 5 numbers get picked) = 5C5 * 44C0 / 49C5

(This is saying the total combinations in which all 5 numbers n the card are chosen times the combinations in which the 44 other numbers are not chosen divided by all possible combinations of 5 numbers from the population of 49)

 

P (4/5 numbers get picked) = 5C4 * 44C1 / 49C5

 

P(0,1,2, or 3 numbers get picked) = 1 - P(5 picked) - P(4 picked)

 

 

A fast check your work on these is using the hypgeom.dist function in Excel. The first one would be =hypgeom.dist(5,5,5,49,FALSE), etc.