Question

15
m = {2, 3, 5, 7, 11, 13}
n = {1, 2, 3, 4, 5, 6, 7, 8}

1. if a number is to be selected at random

from the intersection of set m and n,
what is the probability of choosing an
even number, expressed as a decimal?

1. write the probability of selecting an odd

number from the intersection of set m
and n, expressed as a fraction?

Explanation:

Step1: Find the intersection of sets \(M\) and \(N\)

The intersection of two sets \(M\) and \(N\), denoted as \(M\cap N\), is the set of elements that are common to both \(M\) and \(N\).
\(M\cap N=\{2,3,5,7\}\)
The number of elements in \(M\cap N\), \(n(M\cap N) = 4\)

Step2: Solve for the probability of choosing an even number (for question 1)

The even number in \(M\cap N\) is \(2\). Let \(A\) be the event of choosing an even number. The number of elements in \(A\), \(n(A)=1\)
The probability formula is \(P(A)=\frac{n(A)}{n(M\cap N)}\)
\(P(A)=\frac{1}{4}=0.25\)

Step3: Solve for the probability of choosing an odd number (for question 2)

The odd numbers in \(M\cap N\) are \(3\), \(5\), \(7\). Let \(B\) be the event of choosing an odd number. The number of elements in \(B\), \(n(B) = 3\)
Using the probability formula \(P(B)=\frac{n(B)}{n(M\cap N)}\)
\(P(B)=\frac{3}{4}\)

Answer:

1. \(0.25\)
2. \(\frac{3}{4}\)