ysfpsu wrote:The explanation for this problem in Princeton Review is a little unclear for me so if anyone can help me out, it would be greatly appreciated. The problem is:
A fair 2 sided coin is flipped 6 times. What is the probability that tails will be the result at least twice but more than 5 times?
Here's the correct question:
What is the probability that tails will be the result at least twice but
not more than 5 times?
Good outcomes: 2 tails, 3 tails, 4 tails, or 5 tails.
Bad outcomes: 0 tails, 1 tails, or 6 tails.
P(good outcome) = 1 - P(bad outcome)
Bad outcomes:
P(0 tails):
P(HHHHHH) = 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 1/64.
P(1 tails):
P(THHHHH) = 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 1/64.
Since T could occur on any of the 6 flips, we multiply by 6: 6 * 1/64 = 6/64.
P(6 tails):
P(TTTTTT) = 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 1/64.
Since any of the above would be a bad outcome, we add the fractions:
P(bad outcome) = 1/64 + 6/64 + 1/64 = 8/64 = 1/8.
Thus, P(good outcome) = 1 - 1/8 = 7/8.
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