State yes/no in each part, and explain in a sentence or two. a. You have a bowl

Question

State 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? 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? c. A soccer player is going to take a penalty kick 50 times at practice. They are interested in the number of shots they make (each kick is either made or missed). If each kick attempt is independent with a 35% chance (0.35 probability) of being made, then is the total number of kicks made in the 50 attempts following a binomial distribution? d. A basketball player is going to take 50 free throws at practice. They are interested in the number of shots they make (each shot is either made or missed). If shot attempts are independent, but the player begins to shoot better the more they attempt shots (the probability they make a shot increases the more attempts they take, p is increasing), then is the total number of shots made in the 50 attempts following a binomial distribution? e. Your teacher has a stack of 3 times 5 cards, which have the names of each of the students in your class on it (including you). The teacher randomly select a card, asks the student a question, and sets the card aside. The teacher then randomly selects another card. Is the probability that the second pick is you independent of what the first name was? f. Your teacher has a stack of 3 times 5 cards, which have the names of each of the students in your class on it (including you). The teacher randomly select a card, asks the student a question, puts the card back in the stack, and shuffles the cards. The teacher then randomly selects another card Is the probability that the second pick is you independent of what the first name was?

Explanation / Answer

a:

No becuase after selecting first number of balls remaining in the bowl is 99. So probability of selecting of second blue ball is depend upon color of first ball.

b:

Yes, beucase balls are drawn with replacement.

c:

Yes

Trials are independent.

Probability of success remain same in each trial.

Each trial has only two possible outcomes.

SO it is a binomial distribution.

d:

No

Trials are independent.

Probability of success is changing in each trial.

Each trial has only two possible outcomes.

SO it is not a binomial distribution.

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