1.(5 points) Calculate the odds of winning the Power Ball $100 prize. In order to win, you must match 4 of the 5 winning white balls numbered 1 to 69, and NOT match the red power ball numbered 1 to 26. Write the final answer as a ratio instead of decimal fraction. For example, write instead of 0.25. 1/10 instead of 0.10. Note: There are 2 separate bags - one with the 69 white balls and another with the 26 red balls. For the white balls, we are picking WITHOUT replacement. (Note: If necessary, draw a bag with 69 balls in it and mark 5 balls as the winning balls. As you draw each ball out of the bag, cross out that ball in your bag. Draw another bag with 26 red balls and mark one ball as the winning power ball.)

a.What is the probability of picking any of the 5 winning white balls from the bag for your 1^st pick?

b.What is the probability of picking any of the 4 remaining winning white balls from the bag for your 2^nd pick?

c.What is the probability of picking any of the 3 remaining winning white balls from the bag for your 3^rd pick?

d.What is the probability of picking any of the 2 remaining winning white balls from the bag for your 4^th pick?

e.What is the probability of NOT picking the last winning white ball from the bag for your 5^th pick?

f.What is the probability of NOT picking the winning red power ball from the other bag?

g.Now we can pick the 4 winning white balls in any order. To account for this, we must multiply by a factor F = 5!/[4! * 1!]. What is F?

Using the multiplication rule for the numbers you got for a-g, what is the probability of winning the Power Ball $100 prize? (Note: The Power Ball ticket says the probability of winning are 1/36,525. If you do not get something close to this number, then you did something wrong!)

3. (5 points) Calculate the odds of winning the Power Ball $100 prize. In order to win, you must match 4 of the 5 winning white balls numbered 1 to 69, and NOT match the red power ball numbered 1 to 26. Write your final answer as a ratio instead of decimal fraction. For example, write 1/4 instead of 0.25. 1/10 instead of 0.10. Note: There are 2 separate bags - one with the 69 white balls and another with the 26 red balls. For the white balls, we are picking WITHOUT replacement. (Note: If necessary, draw a bag with 69 balls in it and mark 5 balls as the winning balls. As you draw each ball out of the bag, cross out that ball in your bag. Draw another bag with 26 red balls and mark one ball as the winning power ball.)| a. What is the probability of picking any of the 5 winning white balls from the bag for your 1st pick? b. What is the probability of picking any of the 4 remaining winning white balls from the bag for your 2nd pick? c. What is the probability of picking any of the 3 remaining winning white balls from the bag for your 3"d pick? d. What is the probability of picking any of the 2 remaining winning white balls from the bag for your 4th pick? e. What is the probability of NOT picking the last winning white ball from the bag for your 5 pick? f. What is the probability of NOT picking the winning red power ball from the other bag? g. Now we can pick the 4 winning white balls in any order. To account for this, we must multiply by a factor F = 51/[4! * 1!]. What is F? h. Using the multiplication rule for the numbers you got for a-g, what is the probability of winning the Power Ball $100 prize? (Note: The Power Ball ticket says the probability of winning are 1/36,525. If you do not get something close to this number, then you did something wrong!)