Question

If a standard dice ius rolled 50 times what s the theretical probibility of rolling a 4

Answer 1

We seems to be being asked the probability of rolling at least one four in fifty tries, which should be pretty high. As usual with "at least" questions, we write

p = P(at least one 4) = 1 - P(no fours at all)

The probability of a four on one roll is of course 1/6, so the probability for "not a four" is 1-1/6=5/6. We want the probability of a conjunction of 50 independent events: no four on the first roll and no four on the second roll and...

For a conjunction of independent events we multiply their probabilities. That's 5/6 times itself 50 times. So our answer is

`p = 1 - \left( \frac 5 6 \right)^(50)`

If we need a decimal approximation, it's

`p \approx 0.999890 = 99.9890\%`