HW3_solution.pdf - STAT 67 Fall 2016 Homework 3 1 5 points...

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STAT 67, Fall 2016 Homework 3 10-21-2016 1. 5 points each. States yes/no in each part, and explain in a sentence or two. a. You have a bowl filled with 100 balls, which are colored red or blue. You have 50 red and 50 blue balls. You randomly select a ball and throw it out (don’t put it back in the bowl). Then you go to randomly select another ball. Is the probability that the second pick is blue independent of what the first ball color was? No. P(2nd pick is blue | 1st is blue)=49/99 and P(2nd pick is blue | 1st is red)=50/99. This is to imply that the probability of the 2nd pick being blue depends on what the first pick was. b. You have a bowl filled with 100 balls, which are colored red or blue. You have 50 red and 50 blue balls. You randomly select a ball, record the color, and put the ball back into the bowl. Then you go to randomly select another ball. Is the probability that the second pick is blue independent of what the first ball color was? Yes. Since you put the ball back, the probability of the second pick being blue is 50/100 regardless of what the first pick was. c. A basketball player is going to shoot the ball 25 times. They are interested in the number of shots they make (each shot is either made or missed). If each shot attempt is independent with a 95% chance (0.95 probability) of being made, then is the total number of shots made in the 25 attempts following a binomial distribution? Yes. This is the definition of a binomial random variable. The trials are independent and the probability of success is constant.
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