Respuesta :

DeanR

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

[tex]p = 1 - \left( \frac 5 6 \right)^{50}[/tex]

If we need a decimal approximation, it's

[tex]p \approx 0.999890 = 99.9890\%[/tex]