Question

Let S = {5, 10, 15, ⋯ ⋯ ⋯ ⋯ ,90, 95, 100}.When a number is randomly chosen from the set S,
let the random variable X represent the value of the chosen number.
(a) [10 points] Find P(X ≤ 90).
(b) [10 points] Find P(X ≤ 20 | X is odd).

Answer 1

Number of elements in S = 20

(a) Set of elements where X <= 90 is {5, 10, 15, ..., 85, 90}.

Number of elements in which follow X <= 90 is 18.

Hence P(X <= 90) = 18/20 = 0.9

(b) P(X <= 20|X is odd) = P(X <= 20 and X is odd)/P(X is odd)

Set of elements where X <= 20 and X is odd = {5, 15}

Number of elements where X <= 20 and X is odd = 2

Hence, P(X <= 20 and X is odd) = 2/20

Set of elements where X is odd = {5, 15, 25, ... , 85, 95}

Number of elements where X is odd = 10

Hence, P(X is odd) = 10/20

P(X <= 20|X is odd) = P(X <= 20 and X is odd)/P(X is odd) = (2/20)/(10/20) = 2/10 = 0.2