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?
To determine if the events "odd" and "yellow" are independent, we need to see if the probability of an odd number being on a yellow slip is the same regardless of whether the number is on a white or yellow slip.
Given that there are 16 white slips and 4 yellow slips, the probability of randomly selecting a white slip is 16/20 = 4/5, and the probability of randomly selecting a yellow slip is 4/20 = 1/5.
Now let's calculate the conditional probabilities:
- Probability of selecting an odd number given that the slip is white: 8 (odd numbers on white slips) / 16 (total white slips) = 1/2
- Probability of selecting an odd number given that the slip is yellow: 4 (odd numbers on yellow slips) / 4 (total yellow slips) = 1
Since the probabilities of selecting an odd number on a white slip and on a yellow slip are different, the events "odd" and "yellow" are not independent.