2. Describe the sample space (2) for the following experiments and provide its size. State and justify whether the corresponding probability space is uniform or not. (a) Throwing 3 fair dice. (b) A bag contains 3 red balls and 1 blue ball. Two random balls are drawn one by one (without putting the first ball back in the bag) and their color is examined. (c) Picking a random ball from the bag as above, but putting it back this time before picking another ball. (d) A random walk on the x-axis starts at r = 0. At each step, you move +1 (right) or -1 (left) with equal probability. You move as described for 3 steps and then examine your final position on the x-axis. For example, if you move right 2 times and then left once, you end up at position 1. 1 3. For the sample spaces in Question 2, describe the events AUB and AnB, where A and B are as follows. Be precise in your answers and simplify them where possible (e.g., if an event consists of only one particular outcome, specify this outcome). = (a) A "At least one of the dice shows a 6", B = "The dice show the same number". (b) A "At least one of the balls drawn is blue", B = "Both balls have the same color". (c) A= "At least one of the balls drawn is blue", B = "Both balls have the same color". (d) A= "You end up at x 1", B = "The first move is left".
2. Describe the sample space (2) for the following experiments and provide its size. State and justify whether the corresponding probability space is uniform or not. (a) Throwing 3 fair dice. (b) A bag contains 3 red balls and 1 blue ball. Two random balls are drawn one by one (without putting the first ball back in the bag) and their color is examined. (c) Picking a random ball from the bag as above, but putting it back this time before picking another ball. (d) A random walk on the x-axis starts at r = 0. At each step, you move +1 (right) or -1 (left) with equal probability. You move as described for 3 steps and then examine your final position on the x-axis. For example, if you move right 2 times and then left once, you end up at position 1. 1 3. For the sample spaces in Question 2, describe the events AUB and AnB, where A and B are as follows. Be precise in your answers and simplify them where possible (e.g., if an event consists of only one particular outcome, specify this outcome). = (a) A "At least one of the dice shows a 6", B = "The dice show the same number". (b) A "At least one of the balls drawn is blue", B = "Both balls have the same color". (c) A= "At least one of the balls drawn is blue", B = "Both balls have the same color". (d) A= "You end up at x 1", B = "The first move is left".
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 50E: Flexible Work Hours In a recent survey, people were asked whether they would prefer to work flexible...
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Transcribed Image Text:2. Describe the sample space (2) for the following experiments and provide its size. State
and justify whether the corresponding probability space is uniform or not.
(a) Throwing 3 fair dice.
(b) A bag contains 3 red balls and 1 blue ball. Two random balls are drawn one by one
(without putting the first ball back in the bag) and their color is examined.
(c) Picking a random ball from the bag as above, but putting it back this time before
picking another ball.
(d) A random walk on the x-axis starts at r = 0. At each step, you move +1 (right) or
-1 (left) with equal probability. You move as described for 3 steps and then examine
your final position on the x-axis. For example, if you move right 2 times and then left
once, you end up at position 1.
1
3. For the sample spaces in Question 2, describe the events AUB and AnB, where A and
B are as follows. Be precise in your answers and simplify them where possible (e.g., if an
event consists of only one particular outcome, specify this outcome).
=
(a) A "At least one of the dice shows a 6", B = "The dice show the same number".
(b) A "At least one of the balls drawn is blue", B = "Both balls have the same color".
(c) A= "At least one of the balls drawn is blue", B = "Both balls have the same color".
(d) A= "You end up at x 1", B = "The first move is left".
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