Say you need to win 4 times in a row at a 25% success chance for each event, how do I calculate the chance of winning? Overall, how does this calculation goes? given that 1st is a win, what is the chance that my second is a win, third, fourth etc. (Consider the events to be independent and can go for an infinity amount trials)
[Math] 25% chance of happening but has to happen 4 times in a row, what is the real chance of happening
probability
Best Answer
Given the first is won, the chance that the second is won is the same chance you had of winning the first, since the events are independent. To find the probability of getting 4 wins in a row, multiply the probability of a single win in each term by each other. So, if there is a 0.25 change of winning each round, the equation should appear as below: $$ 0.25 \times 0.25 \times 0.25 \times 0.25 $$ To make the multiplying a bit easier, let's use fractions (multiplying 4s is easier than multiplying 25s): $$ \frac{1}{4} \times \frac{1}{4} \times \frac{1}{4} \times \frac{1}{4} = \frac{1}{256} $$ So, the probability of winning (by getting 4 wins in a row) is $ \frac{1}{256} $