Question

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(b)

p(b) =
(simplify your answer.)

Explanation:

Step1: Identify elements in event B

The multiples of 4 in the set \(S = \{1,2,\cdots,15\}\) are 4, 8, 12. So \(n(B)=3\).

Step2: Identify size of sample - space

The size of the sample - space \(S\) is \(n(S)=15\).

Step3: Calculate probability

The probability formula is \(P(B)=\frac{n(B)}{n(S)}\). Substituting \(n(B) = 3\) and \(n(S)=15\) into the formula, we get \(P(B)=\frac{3}{15}\). Simplifying the fraction, we have \(P(B)=\frac{1}{5}\).

Answer:

\(\frac{1}{5}\)