elias writes the numbers 1 through 20 on separate slips of paper. there are 16 white slips of paper and four…

elias writes the numbers 1 through 20 on separate slips of paper. there are 16 white slips of paper and four yellow slips of paper. there are eight odd numbers on white slips, and the rest of the odd numbers are on yellow slips. are the events “odd” and “yellow” independent?\nno, because the probability of choosing a yellow slip is not equal to the probability of choosing a yellow slip given an odd number\nno, because the probability of choosing an odd number is not equal to the probability of choosing an odd number on a yellow slip\nyes, because the probability of choosing an odd number is equal to the probability of choosing an odd number given that the slip is yellow\nyes, because the probability of choosing an odd number on a yellow slip of paper is equal to the probability of choosing an odd number

elias writes the numbers 1 through 20 on separate slips of paper. there are 16 white slips of paper and four yellow slips of paper. there are eight odd numbers on white slips, and the rest of the odd numbers are on yellow slips. are the events “odd” and “yellow” independent?\nno, because the probability of choosing a yellow slip is not equal to the probability of choosing a yellow slip given an odd number\nno, because the probability of choosing an odd number is not equal to the probability of choosing an odd number on a yellow slip\nyes, because the probability of choosing an odd number is equal to the probability of choosing an odd number given that the slip is yellow\nyes, because the probability of choosing an odd number on a yellow slip of paper is equal to the probability of choosing an odd number

Answer

Explanation:

Step1: Calculate probability of choosing an odd number

There are 10 odd numbers from 1 - 20. Total number of slips is 20. So $P(\text{odd})=\frac{10}{20}=\frac{1}{2}$.

Step2: Calculate probability of choosing an odd number given slip is yellow

There are 4 yellow slips. Number of odd - numbered yellow slips is $10 - 8=2$. So $P(\text{odd}|\text{yellow})=\frac{2}{4}=\frac{1}{2}$.

Step3: Check independence condition

Two events $A$ and $B$ are independent if $P(A)=P(A|B)$. Here, $A$ is the event of choosing an odd number and $B$ is the event of choosing a yellow slip. Since $P(\text{odd}) = P(\text{odd}|\text{yellow})=\frac{1}{2}$, the events "odd" and "yellow" are independent.

Answer:

yes, because the probability of choosing an odd number is equal to the probability of choosing an odd number given that the slip is yellow