EricKryk wrote:The probability is 1/2 that a certain coin will turn up heads on any given toss. If the coin is to be tossed three times, what is the probability that on at least one of the tosses the coin will turn up tails?
A) 1/8
B) 1/2
C) 3/4
D) 7/8
E) 15/16
Slightly different approach:
Good ways = total ways - bad ways.
Total ways:
Number of options for the first toss = 2. (Heads or tails.)
Number of options for the second toss = 2. (Heads or tails.)
Number of options for the third toss = 2. (Heads or tails.)
To combine these options, we multiply:
2*2*2 = 8.
Bad ways:
Of the 8 ways to toss the coin, only 1 way will yield NO TAILS:
HHH.
Good ways:
Total ways - bad ways = 8-1 = 7.
Resulting probability:
(good ways)/(total ways) = 7/8.
The correct answer is
D.
Another option is to WRITE OUT all of the ways to toss the coin 3 times:
HHH
HHT
HTH
HTT
TTT
TTH
THH
THT
Of the 8 ways above, the 7 options in red each include at least one tails.
Thus, P(at least one tails) = 7/8.
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