OEIf Dipak still has money after the third hand, then he must have won at least one of the hands, and possibly more than one. However, directly calculating the probability that he wins at least one hand is tricky because there are so many ways it could happen (for example, he could lose-lose-win, or W-W-L or W-L-W or L-W-L, and so on). So think about it this way: the question asks for the probability that he will win at least one hand. What if he doesn’t? That would mean that he doesn’t win any hands at all. If we calculate the probability that he loses every hand, we can then subtract that from 1 and find the corresponding probability that he wins at least one hand. Since Dipak has a 25% chance of winning each hand, this means that he has a 75% chance of losing it, or 3/4 (the answers are in fractions, so it’s best to work with fractions). To find the probability that he loses all three hands, simply multiply the probabilities of his losing each individual hand. 3/4*3/4*3/4=27/64.
Subtracting this from 1 gives you the answer you’re looking for:1-27/64=37/64
D is the answer
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