Estimating Probabilities

Believe it or not, a question as wacky as the following can and allegedly does show up on the Series 65/66 exams:

You have flipped a coin 100 times now. It has come up tails 68 times. If you flip the coin again, the probability of its landing "tails" is

A. 32%

B. 69%

C. 68.5%

D. 50%

EXPLANATION: I was tutoring a man who lives a few blocks from the Las Vegas strip. Man, did he have a hard time answering this question. "Well," he pushed back, "who's flipping the coin?" "What KIND of coin are we talking about here?" "Which casino is he in?"

Eventually, he--like you--figured out that if there are two outcomes, the probability is always 50%, period. End of story.

Also, note that if a coin turns up 7 out of 10 times heads, that is nowhere as freaky as a coin that comes up heads 650 times out of 1,000. The law of large numbers says that as the number of flips increases, the outcome should get closer to 50%. Why is this on the test? Financial planners talk about this stuff to help themselves understand why investing clients are so horrible at estimating and understanding risk.

ANSWER: d