Question

construct a probabilty distribution table for a binomial experiment of rolling a fair die 5 times and observing the number of times a 3 is rolled.

Answer 1

Sample size, n = 5

Probability of 3 in roll of a die = 1/6 = 0.1667

Binomial distribution formula:

P(x) = n!/(x!*(n-x)!) * pˣ * (1-p)ⁿ⁻ˣ

Probability distribution table:

X	Formula	P(X)
0	5!/(0!* 5!) * 0.1667^0 * 0.8333^5	0.4018
1	5!/(1!* 4!) * 0.1667^1 * 0.8333^4	0.4019
2	5!/(2!* 3!) * 0.1667^2 * 0.8333^3	0.1608
3	5!/(3!* 2!) * 0.1667^3 * 0.8333^2	0.0322
4	5!/(4!* 1!) * 0.1667^4 * 0.8333^1	0.0032
5	5!/(5!* 0!) * 0.1667^5 * 0.8333^0	0.0001