Question

When a fair die is rolled, it has equal chance to show one of six faces, labelled 1 through 6. If it is rolled 10 times, what is the probability that there are at least three 6's?

Answer 1

TOPIC:Binomial distribution.

=> Define, = P (of getting a 6 in a soll) wool) = There are total 6 Now, n = No. of times, the die was rolled. / possible outcomes in the die and the outcomes are equally likely = 10. Let, x = The no. times, 6's being obtained out of the 10 rolls of the die. Here in' is fined, the die is rolled independently and the value of '' remains the same for each soll, X ~ Bin (n=10, p = 16 So, the proof of x is *-* () C)*(+)10-27 P(x2x) = { (M) p* (1-1) Jorn x=0,1,–, 10. 0 ; otherwise. . We need P[x of getting at least three 62 z [x is at least 3 & P Law of - 1-P (x<3. [ complementation 21-P (xs

= 1- [P(x=0) +P(x =D +P(x=2) --[(0)4+)* (33" + (1999 +(2) (+)?( By the bol of x 0 2248 (in four decimale. (Aus)