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Probability problem

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Hi guys, by this time all I've done was read read read... but now I have to write, cause I can't find logical solution to this problem.

Have been reading "Probability tutorial" by Walker here on forum, and came across this:

Mutually exclusive events

Q: If Jessica rolls a die, what is the probability of getting at least a "3"?
Solution: There are 4 outcomes that satisfy our condition (at least 3): {3, 4, 5, 6}. The probability of each outcome is 1/6. The probability of getting at least a "3" is:
P = 1/6+ 1/6 + 1/6 + 1/6 = 2/3

Meanwhile
In "Kaplan premier 2013" chapter16, p814

Same principal is being tested but the way of getting there is cosmically different:

If a fair coin is flipped three times, what is the probability of getting at least one tail ?
Suggested way of tackling this one is:

Total - Undesired

1 - HHH
1- 1/2*1/2*1/2

1-1/8

= 7/8

Please advise

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