from the sample space s={1,2,3,4,...,15} a single number is to be selected at random. given the following…
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(a and c) p(a and c)= (simplify your answer. type an integer or a fraction.)
Answer
Explanation:
Step1: List elements of event A and C
Event A (even numbers in S): $A={2,4,6,8,10,12,14}$. Event C (prime numbers in S): $C = {2,3,5,7,11,13}$.
Step2: Find intersection of A and C
The intersection $A\cap C$ is the set of elements that are in both A and C. So $A\cap C={2}$.
Step3: Calculate probability
The probability formula is $P(E)=\frac{n(E)}{n(S)}$, where $n(E)$ is the number of elements in event E and $n(S)$ is the number of elements in the sample - space. Here, $n(A\cap C) = 1$ and $n(S)=15$. So $P(A\cap C)=\frac{1}{15}$.
Answer:
$\frac{1}{15}$