Question

1. In an instant lottery, your chances of winning are 0.1. If you play the lottery six times and outcomes are independent, determine the probability that

(i) you win at most once.

(ii) you lose all six times.

(iii) you win exactly two times.

Please show work will rate!!!

Answer 1

p = 0.1

n = 6

This is a binomial distribution

P(X = x) = 6Cx * 0.1^x * (1 - 0.1)^6-x

i) P(X < 1) = P(X = 0) + P(X = 1)

                 = 6C0 * 0.1⁰ * 0.9⁶ + 6C1 * 0.1¹ * 0.9⁵

                 = 0.8857

ii) P(lose all 6) = (win 0)

                        = P(X = 0)

                        = 6C0 * 0.1⁰ * 0.9⁶

                        = 0.5314

iii) P(X = 2) = 6C0 * 0.1² * 0.9⁴

                   = 0.0984