Northeastern Illinois University Probability of Winning the Powerball Questions

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1.I roll a weighted (unfair) six sided die. The probabilities of getting a 1, 2, 3, or 4 are all the same. Getting a 5 is twice as likely as getting a 4. Getting a 6 is twice as likely as getting a 5. What is the probability of getting a 3?
2.I have 50 index cards. Each is labeled a letter from A to E and with an integer between 0 and 9. The 50 cards are: {A0, A1, A2, A3, A4, A5, A6, A7, A8, A9, B0, B1, B2, B3, B4, B5, B6, B7, B8, B9, C0, C1, C2, C3, C4, C5, C6, C7, C8, C9, D0, D1, D2, D3, D4, D5, D6, D7, D8, D9, E0, E1, E2, E3, E4, E5, E6, E7, E8, E9}. I pick 6 of these cards at random. What is the probability that one of my six cards is “E4” ?
3.What is the probability of winning the POWERBALL if there are 70 ping pong balls blowing around randomly, and you need to predict the numbers of the six that roll out? (The order does not matter).

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