Question

7. 1/ 3 points | Previous Answers WaneF MAC7 8.4.029 My Notes Ask Your Teacher The Sorry State Lottery requires you to select five different numbers from 0 through 51. (Order is not important.) You are a Big Winner if the iv numbers you select agree with those in the drawing and you are a Small-Fry Winner if four of your five numbers agree with those in the drawing. (Enter your answers as exact answers.) What is the probability of being a Big Winner? 1/2598960 What is the probability of being a Small-Fry Winner? /519792X What is the probability that you are either a Big Winner or a Small-Fry Winner? /433160X Need Help?Readin Read It 8. o1 points 1 Previous Answers WaneFMAC7 8.4.033. My Notes Ask Your Teacher In a New York State daily lottery game, a sequence of four digits (not necessarily different) in the range 0-9 are selected at random. Find the probability that all four are different. 5040 Need Help?Read It Watch

Please answer both!

Answer 1

Question 7

a)

Number of ways to win: 1
Number of possible outcomes: 52P5 = 2598960
P(winner) = 1/ 2598960

b)

There are 5C4 ways to get any 4 out of 5 of these numbers and there are 47C1 ways to get any 5th number that is not part of the Big Win combination.

Therefore the probability of being a Small-Fry winner = (5C4 * 47C1) / 52C5

5C4 = 5! / (4! *1!) = 5

47C1 = 47! / (1! * 46!) = 47

52C5 = 2598960

Therefore P(Small Fry) = (5 * 47) / 2598960
= 235 / 2598960
=235 / 2598960

=47 /519792

c)

Hence,

P(big or small) = 1/ 2598960 + 47 /519792

= 0.0000908

Question 8

Total number of cases = 10^4 = 10,000

T0he first digit can be ANYTHING.

The second digit has a 9/10 chance of being different from the first.

The third digit has an 8/10 chance of being different from the first AND from the second.

The fourth digit has a 7/10 chance of being different from the first, second, AND third digit.

= 9/10 * 8/10 * 7/10

= 504/1000.

= 63/125,