Hi ZS, assuming that whether or not one wins or loses on one scratch ticket (what is that, in either case?) is independent from winning or losing on additional scratch ticket, you treat each event as a separate event. Laws of probability tell us to multiply the various probabilities of independent events. It appears that the probability of [losing] on any particular scratch ticket must be 2/3. Prevails the odds of [losing] on 30 scratch tickets consecutively (if it is exactly what your problem is asking) must be (2/3)^30 = approximately 5.2 x 10^-6, which is about.0000052, or 52 the particular 10 million, which comes from 1 chance out of 192,307.
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The Powerball lottery calculations are considering a 1/59 for a five white balls and 1/39 for your “red” power ball. Very first set of multipliers is 59x58x57x56x55. This group totals 600,766,320. Now divide 600,766,360 by 120 (1x2x3x4x5). Increased total is 5,006,386. Actual a 1/39 chance to find the “red” ball. 39 x 5,006,386 gives you the real likelihood of winning the Powerball Jackpot, namely 195,249,054 to 1.
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