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1 Three balls are numbered 1, 2, 3 and placed in a bag. A ball is chosen, its number recorded, then the ball placed back in the bag. This process is repeated twice more. The resulting 3 recorded numbers are added.
Bob walks in the room after the three numbers have been recorded and is told only that the sum of the numbers is 6. Bob announces, "Oh, then they must all have been 2's." What is the probability that Bob is correct?

2 We roll a fair 6-sided die 5 times. What is the probability that we get an odd number in exactly 4 of the 5 rolls?

3 We flip a fair coin 10 times. What is the probability that we get heads in exactly 8 of the 10 flips

May 26, 2020

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1 Three balls are numbered 1, 2, 3 and placed in a bag. A ball is chosen, its number recorded, then the ball placed back in the bag. This process is repeated twice more. The resulting 3 recorded numbers are added.
Bob walks in the room after the three numbers have been recorded and is told only that the sum of the numbers is 6. Bob announces, "Oh, then they must all have been 2's." What is the probability that Bob is correct?

There are 7 possibilities:

222

123

132

213

231

312

321

Probability that Bob is correct = 1/7.

May 26, 2020