Calculate the odds of winning the Mega Millions 2nd prize of $1 million. In orde

Question

Calculate the odds of winning the Mega Millions 2nd prize of $1 million. In order to win, you must match the numbers of 5 white balls numbered 1 to 75, and match the yellow Mega ball numbered 1 to 15. Write your final answer in 1/p instead of the fraction p. For example, ¼ = 4. 0.10 = 10. Note: There are 2 separate bags – one with the 75 white balls and another with the 15 yellow balls. For the white balls, we are picking without replacement.

a. What is the probability of picking 1 of the 5 winning white balls from the bag?

b. What is the probability of picking 1 of the remaining 4 winning white balls from the bag?

c. What is the probability of picking 1 of the remaining 3 winning white balls from the bag?

d. What is the probability of picking 1 of the remaining 2 winning white balls from the bag?

e. What is the probability of picking the last remaining winning white ball from the bag?

f. What is the probability of NOT picking the winning yellow Mega ball from the other bag?

g. Using the multiplication rule, what is the probability of winning the Mega Millions 2nd prize in 1/p? (Note: The Mega Millions ticket says the odds of winning are 1 out of 18,492,204. If you do not get something close to this number, then you did something wrong!)

Explanation / Answer

a)  probability of picking 1 of the 5 winning white balls from the bag =5/75

b)  probability of picking 1 of the remaining 4 winning white balls from the bag =4/74

c)probability of picking 1 of the remaining 3 winning white balls from the bag =3/73

d)probability of picking 1 of the remaining 2 winning white balls from the bag=2/72

e)probability of picking 1 of the remaining 3 winning white balls from the bag =1/71

f)probability of NOT picking the winning yellow Mega ball from the other bag =14/25

g) probability of winning the Mega Millions 2nd prize =(5/75)*(4/74)*(3/73)*(2/72)*(1/71)*(14/15)

=1680/31066902000

therefore 1/p =31066902000/1680 =~18492204

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