What Are the Odds of Winning Specific Prizes in Euromillions?

[mynameisfunk]

Homework Statement

Euromillions is a transnational lottery. A player selects 5 "main" numbers without replacement, ignoring order from 1 to 50. The player then selects 2 "lucky star" numbers without replacement and ignoring order from 1 to 11. Ultimately, 5 numbers are randomly selected without replacement ignoring order from 1 to 50 and independently, 2 numbers are selected without replacement from 1 to 11. Consider events (A) the player matches 2 "main" numbers and 1 "lucky star" number and (B) the player matches 1 "main" number and 2 "lucky star" numbers. Separately compute the probabilities of A & B. Which are more likely?

Homework Equations

Hyper geometric Distribution and additiive probability?

The Attempt at a Solution

Sorry for no latex, I couldn't seem to figure it out for the hypergeometric..

A: I had [(5 choose 2)*(45 choose 3)]/(50 choose 5) + [(2 choose 1)*(9 choose 1)]/(11 choose 2)=.39

B: I had [(5 choose 1)*(45 choose 4)]/(50 choose 5) + [(2 choose 2)*(9 choose 0)]/(11 choose 2)=.37


Not sure if this is right..

 

[haruspex]

A: I had [(5 choose 2)*(45 choose 3)]/(50 choose 5) + [(2 choose 1)*(9 choose 1)]/(11 choose 2)=.39

(Assuming the question means exactly 2 main numbers, etc., not at least 2...)
Not a bad start, but think again about how to combine the two probabilities. You want the probability of two independent events both happening.