Question

when rolling 10 dice, what is the probability of rolling 7 sixes? how does this compare to the probability of rolling 7 dice with five or higher? explain the difference.

Answer 1

Rolling 7 sixes,
Here, n = 10, p = 0.167, (1 - p) = 0.833 and x = 7
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 7)
P(X = 7) = 10C7 * 0.167^7 * 0.833^3
P(X = 7) = 0.0003

Rolling 7 with 5 or higher,
Here, n = 10, p = 0.333, (1 - p) = 0.667 and x = 7
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 7)
P(X = 7) = 10C7 * 0.333^7 * 0.667^3
P(X = 7) = 0.0162

In the case of rolling six, the p = 1/6 = 0.167 and

in the case of rolling 5 or higher, the p = 2/6 = 0.333