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At that place's ii lotteries. Each with its ain fix of probabilities. Notice the probabilities for winning change subsequently every draw.

Describe Lottery ane (p) Lottery 2 (p)
ane 0.5 0.25
2 0.4 0.55
3 0.two 0.8
4 0 ane

Person1 draws from Lottery ane and Person2 draws from Lottery two. At the aforementioned time, they each describe one ticket at a time. Once somebody wins, the game ends.

  1. Which person is more likely going to win?
  2. How do y'all compute that?
  3. Can you generalize information technology to whatever probabilities and any number of lotteries?

asked yesterday

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12

  • $\begingroup$ Are the 2 lotteries contained of each other - i.e. does person 1 winning their lottery bear upon person 2'southward gamble of winning theirs? $\endgroup$

    yesterday

  • $\begingroup$ Practice the two people take turns drawing (with Person 1 going first)? If they make draws at the same time, what happens when they both win on the same draw? $\endgroup$

    yesterday

  • $\begingroup$ @ConMan The lotteries are independent. The odds listed are the odds. $\endgroup$

    yesterday

  • $\begingroup$ Equally a nitpick, the words "odds" and "probability" although related are not synonymous. They mean different things. The probability of rolling a six on a standard off-white die is $\frac{i}{6}$. The odds of that occurring notwithstanding are $1:five$. $\endgroup$

    23 hours ago

  • $\begingroup$ The fully generalized formula can be a bit frustrating to read... just the gist of it is that we intermission into cases based on which round the game ends on. For the game to accept ended in round $i$ the previous rounds must have all concluded with neither person winning and in the $i$'th round at least one person winning. Letting $p_i$ exist the probability of person1 winning on round $i$ and $q_i$ the probability of person2 winning on round $i$, the probability of person1 winning is $\sum\limits_{i=i}^\infty p_i\prod\limits_{k=1}^{i-1}(1-p_k)(1-q_k)$. Similarly for person2, swapping $p$'south for $q$'s. $\endgroup$

    23 hours agone