I can find information on calculating the probability of dependent and independent events, but I'm having trouble synthesizing this information in order to calculate the probability of both dependent and independent events occurring.

More specifically, I'm trying to determine the probability that some single event happens X times in a row (order doesn't matter here -- they're all the same event), and only then one of a handful of other possible events occur.

The first event has a probability of occurring 2% of the time, so I believe the probability of it occurring 3 out of 3 tries is 0.02 ^ 3. Each of the other events have probabilities of occurring 1%, 1%, 0%, and 2% of the time. Thus my original attempt at solving this problem was 0.02 ^ 3 * (0.01 + 0.01 + 0 + 0.02) = 0.000032%. This solution seems to ignore the fact that the final event must happen on the fourth try. How can I account for this?

  • $\begingroup$ This sounds like conditional probability. Count carefully. $\endgroup$ – K. Jiang Apr 5 '16 at 17:53
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    $\begingroup$ You have presented a somewhat abstract version of the problem. A more concrete version may be helpful, $\endgroup$ – André Nicolas Apr 5 '16 at 17:54
  • $\begingroup$ @AndréNicolas The concrete version would include lots of tedious details, but the short version is: I am working with a digital slot machine and trying to calculate its payout. One piece of this is determining the payout for matching only Wild symbols. In most cases, a set of Wilds followed by some other symbol would be counted as a match for that other symbol, but a handful of symbols do not allow Wild matches and thus the match would be counted as a Wild match instead. $\endgroup$ – Benji Kay Apr 5 '16 at 18:11

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