Question

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 ¼ 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 3rd 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 5th 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?

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!)

Answer 1

Answer:

Given Data

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

P(correct in 1st pick) =

(Out of 69 balls , you are picking one of the 5 balls (winning))

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

P(correct in 2nd pick) =

(Tptal balls available is 68 , number of outcomes you are expecting is 4 - any of the remaining winning balls )

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

  P(correct in 3rd pick) =

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

Similarly , P(correct in 4th pick) =  

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

Similarly , P(correct in 5th pick) =  

(Total ba;;s remaining after first 4 picks will be 65 , out of 65 only 1winning ball is available . So , there are 64 lossing white balls)

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

In order to calculate of picking exactly 4 winning white balls ,

P(4 winning balls ) =

=

Here , out of the 5 picks , we have to select in which picks one will pick winning balls.

So ,

* 5 picks

* one combination of winning picks and loosing picks out of total combinations.

So, one extra factor of was multiplied.

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.

P(picking winning red ball )=

(There is only one winning ball in a bag of 26 balls)

h)  Using the multiplication rule for the numbers you got for a-g, what is the probability of winning the Power Ball $100 prize.

P( winning power ball ) =

=

=