John makes a bet with Donald that he’s able to flip heads on a coin before Donald throws 2 in a die. What’s the probability of Donald winning, considering John begins the game and they play alternately?

Let the probability of tossing an head be and tail , and the probability of tossing any die face other than a 2 be . If we consider the outcome of John winning, then:

outcome | probability |
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… |

Therefore, the converse probability is given by:

Since this is a geometric series with , then , so: