Question

If a fair die is rolled 7 times, what is the probability, rounded to the nearest thousandth, of getting at least 5 twos?

Answer 1

Case: Binomial Probability

Method:

The formula for the probability is:

`P=^nC_rp^rq^(n-r)`

number of rolls, n= 7

required outcomes, r>= 5

prob of obtaining a 5, p= 1/6

prob of not obtaining a 5, q= 5/6

Hence:

`\begin{gathered} 7C5.((1)/(6))^5((5)/(6))^2+7C6.((1)/(6))^6((5)/(6))^1+7C7.((1)/(6))^7((5)/(6))^0 \\ (21*25)/(6^7)+(7*5)/(6^7)+(1*1)/(6^7) \\ (525+35+1)/(6^7) \\ (561)/(6^7) \\ =0.002 \end{gathered}`

Final answer:

The probability of obtaining at least 5 twos is: 0.002