Probability Grade 12 Data Management Question

Question

Hi I need help with this question: (I just want to know if I got the right answer)

Suppose you buy a lottery ticket for which you choose five different numbers between 1 and 50 inclusive. The order of the first four numbers is not important. The fifth number is a bonus number. To win first prize, all four regular numbers and the bonus number must match, respectively, the randomly generated winning numbers for the lottery. For the second prize, you must match the bonus number plus three of the regular numbers. 

1. What is the probability of winning the first prize?
2. What is the probability of winning the second prize?

for 1 I got 0.000000094 and for 2 I got 0.00000038. Am i correct? Thank you

Answer 1

Yes on 1 and no on 2.

To go from the answer on 1 to the answer on 2: On 2, based upon the fact that the answer is 4 times the answer on A, my guess is that you forgot to multiply by the fact that you choose 1 of the other 45 numbers as well.

Your answer on B should be 4 * 45 = 180 times your answer on A. If you prefer, you can write this as C(4,3)*C(45,1) = 4 * 45 = 180.