Calculate the odds of winning the Power Ball 2d Prize if $1 million. In order to
ID: 3244070 • Letter: C
Question
Calculate the odds of winning the Power Ball 2d Prize if $1 million. In order to win, you must match the numbers of 5 white balls numbered 1 to 69, and match the red power ball numbered 1 to 26. Write your inal answer in 1/p instead of the fraction p.
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 white balls from the bag?
c. What is the probability of picking 1 of the remaining 3 white balls from the bag?
d. What is the probability of picking 1 of the remaining 2 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 red power ball from the other bag?
g. Using the multiplication rule, what is the probability of winning the Power Ball 2d prize in 1/p? The power ball ticket says the odds of winning are 1 out of 11,688,054. If you didnt close to this number, you did something wrong.
Explanation / Answer
Solution:-
The number of ways 5 numbers can be chosen from 69 = 69C5 = 11,238,513
Out of these 69C5 ways there are 26C1 ways to pick powerball number.
The total number of ways to pick 6 numbers is = 69C5 * 26C1
= 11,238,513 * 26
= 292,201,338
The probability of winning the powerball 2nd prize = 5C5 * 1C1 / 69C5 * 26C1
Therefore, the odds of wining the powerball 2nd prize = 1/292,201,337
a) The probability of picking 1 of the 5 winning white balls = 5C1 / 69C5
= 5 / 11,238,513
b) The probability of picking 1 of the remaining 4 white balls from the bag = 4C1 / 68C5
= 4 / 10,424,128
=
c) The required probability = 3C1 / 67C5 = 3 / 9,657,648
= 1 / 3,219,216
d) The required probability = 2C1 / 66C5
= 2 / 8,936,928 = 1 / 4,468,464
e) The required probability = 1C1 / 65C5
= 1 / 8936928
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