Suppose the rules for the carnival game in Example 4.14 are modified so that the marble drawn each time is returned to the box before the next drawing. a. Redraw the tree diagram drawn for Exercise 4.79, listing the probabilities for the game when played “with replacement.”
b. What is the probability of drawing a red marble on the second drawing? What additional information is needed to find the probability? What effect does this have on P(red on 2nd drawing)?
c. Calculate the probability of winning the $2 prize.
d. Calculate the probability of winning the $5 prize.
e. When the game is played with replacement, is the $2 or the $5 prize harder to win? Which is more likely? Justify your answer.