Question

an urn contains red, black, and green balls. one of the colors is chosen at random (meaning that the chosen color is equally likely to be any of the colors), and then balls are randomly chosen from the urn. let be the number of these balls that are of the chosen color. a. find . b. let equal if the ball selected is of the chosen color, and let it equal otherwise. fi

Answer 1

The question is about probability without replacement from an urn with red, black, and green balls. A variable related to the number of balls of the chosen color is mentioned, but specific probabilities cannot be calculated without more information.

Step-by-step explanation:

The student appears to be asking about probability without replacement. The urn contains an unspecified number of red, black, and green balls, and a color is chosen at random before drawing balls. The letter b seems to represent a variable related to the number of balls of the chosen color. Without more information, a specific expression for b cannot be provided.

Regarding part b of the question, it introduces a binary variable that takes the value 1 if a selected ball is of the chosen color, and 0 otherwise. We would need to know the total number of balls and the number of balls of each color to determine the probability of drawing a ball of the chosen color. Then the expected value of this random variable could be calculated. However, key parts of the question are missing, so I cannot provide a reliable method for calculating this probability.

For example, in an urn with four red and three yellow balls, if three balls are drawn without replacement, the probability that one of each color is selected involves combinations and probabilities of different drawing sequences. The specific question asked cannot be answered without additional information regarding the quantity of each color of balls in the urn.

Answer 2

To find the number of balls that are of the chosen color from an urn, we need to calculate the probability of choosing each color and multiply it by the total number of balls in the urn. The number of balls that are of the chosen color can be represented as a variable that equals zero if the selected ball is not of the chosen color, and the number of balls of the chosen color if the selected ball is of the chosen color.

Step-by-step explanation:

In this problem, we are given an urn that contains red, black, and green balls. One color is chosen at random, and then balls are randomly chosen from the urn. We need to find the number of balls that are of the chosen color. Let's solve this problem step by step:

a. To find the number of balls that are of the chosen color, we need to calculate the probability of choosing each color and then multiply it by the total number of balls in the urn. Let's say the probability of choosing a specific color is p. Then, the expected number of balls of the chosen color is p multiplied by the total number of balls in the urn.

b. Let n be the number of balls that are of the chosen color. We can represent it as: n = if the ball selected is of the chosen color, and n = 0 otherwise. This means that if the ball selected is of the chosen color, then n is equal to the number of balls of the chosen color. Otherwise, n is equal to 0.