from the sample space s = {1, 2, 3, 4, ..., 15} a single number is to be selected at random. given the…

from the sample space s = {1, 2, 3, 4, ..., 15} a single number is to be selected at random. given the following events, find the indicated probability. a: the selected number is even. b: the selected number is a multiple of 4. c: the selected number is a prime number. p(c|a) p(c|a) = (simplify your answer. type an integer or a fraction.)

from the sample space s = {1, 2, 3, 4, ..., 15} a single number is to be selected at random. given the following events, find the indicated probability. a: the selected number is even. b: the selected number is a multiple of 4. c: the selected number is a prime number. p(c|a) p(c|a) = (simplify your answer. type an integer or a fraction.)

Answer

Explanation:

Step1: Find elements in event A

The sample - space (S={1,2,\cdots,15}). The set of even numbers in (S) is (A = {2,4,6,8,10,12,14}), so (n(A)=7).

Step2: Find elements in (A\cap C)

The set of prime numbers in (S) is (C={2,3,5,7,11,13}). The intersection of (A) and (C) is (A\cap C = {2}), so (n(A\cap C)=1).

Step3: Use the formula for conditional probability

The formula for conditional probability is (P(C|A)=\frac{P(A\cap C)}{P(A)}). Since (P(A\cap C)=\frac{n(A\cap C)}{n(S)}) and (P(A)=\frac{n(A)}{n(S)}), then (P(C|A)=\frac{n(A\cap C)}{n(A)}). Substituting (n(A\cap C) = 1) and (n(A)=7) into the formula, we get (P(C|A)=\frac{1}{7}).

Answer:

(\frac{1}{7})