Question

2. State yes/no in each part, and explain in a sentence or two (a) You have a box filled with 400 balls, which are colored black or white. You have 200 black and 200 white balls. You randomly select a ball and throw it out (don't put it back in the box). Then yoiu go to randomly select another ball. Is the probability that the second pick is white independent of what the first ball color was? (b) You have a box filled with 100 balls, which are colored black or white. You have 50 black and 50 white balls. You randomly select a ball, record the color, and put the ball back into the box. Then you go to randomly select another box. Is the probability that the second pick is white independent of what the first ball color was? (c) A soccer player is going to do a free kick 50 times at practice. They are interested in the number of goals they make (each kick is either a goal or not). If each free kick attempt is independent with a 10% chance (0.10 probability) of being a goal, then is the total number of free kicks that is a goal in the 50 attempts following a binomial distribution? (d) A soccer player is going to do 50 penalty kicks at practice. They are interested in the number of goals they make (each goal is either made or missed). If goal attempts are independent, but the player begins to score more goals the more attempts they make (the probability they make a goal increases the more attempts they take, p is increasing), then is the total number of goals made in the 50 attempts following a binomial distribution? (e) Your husband has a box filled with scraps of paper, which have the names of restaurants (including the first place you went out with him). Your husband randomly selects a scrap of paper from the box, reads it out loud, and sets the pape Is the probability that the second pick is the first place you went out with him independent of what the first name was? r aside. Your husband then randomly selects another paper (f) Your wife has a box filled with scraps of paper, which have the names of restaurants (including the first place you went out with her). Your wife randomly selects a scrap of paper from the box reads it out loud, puts the paper back in the hat, and mixes up the scraps of paper. Your wife then randomly selects another paper. Is the probability that the second pick is the first place you went out with her independent of what the first name was?

Answer 1

(a) No because after first selection of ball, total number of ball changes in the box. Therefore, the probability that the second pick is white was not independent of what the first ball color.

(b) Yes because after first selection of ball, total number of ball does not change in the box. Therefore, the probability that the second pick is white was independent of what the first ball color.

(c) Yes because there are only two outcomes, goal or not, there are fixed number of trials, 50, probability of success is constant, 10% chance and trials are independent.

(d) No because probability of success is not constant, the probability they make a goal increases the more attempts they take, p is increasing.