2. In a certain game, you have to defeat three opponents in a row in order to wi

Question

2. In a certain game, you have to defeat three opponents in a row in order to win. In other words, you battle three opponents one after the other, and if any one of them defeats you, you must restart and attempt again to defeat all three. You estimate that opponent 1 can be defeated with probability 4/5, opponent 2 with probability 3/5 and opponent 3 with probability 2/5.

i) Find the probability that you win on the first try, i.e., that you defeat all three without losing to any one of them.

ii) Find the expected number of attempts you need to make before winning. An attempt stops when you either defeat all three opponents, or lose to one opponent and have to restart.

Explanation / Answer

i) Probability that you win on the first try = (4/5)x(3/5)x(2/5) = 0.192

ii) Expected number of attempts you need to make before winning = 1/0.192 = 5.21

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