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[16 marks] ( Lecture 4 ) There are two different and independent lottery games: Lottery A and Lottery B. Mike buys one ticket of Lottery

[16 marks] (Lecture 4) There are two different and independent lottery games: Lottery A and Lottery B. Mike buys one ticket of Lottery A and one ticket of Lottery B. For the ticket of Lottery A, the chance of winning is 15%; for the ticket of Lottery B, the chance of winning is 10%. Answer the following questions:

What is the probability that Mike wins both lotteries?
What is the probability that Mike wins at least one of the lotteries?
What is the probability that Mike wins just one of the lotteries?
What is the probability that Mike not wins any of the lotteries?
Given that Mike wins at least one of the lotteries, what is the probability that he wins Lottery A?

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