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A certain coin with heads on one side and tails on the other
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30 Jul 2018, 10:56
30 Jul 2018, 10:56
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Question Stats:
82% (00:49) correct
17% (00:47) wrong based on 90 sessions
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A certain coin with heads on one side and tails on the other has a \(\frac{1}{2}\) probability of landing on heads. If the coin is flipped three times, what is the probability of flipping 2 tails and 1 head, in any order?
(A) \(\frac{1}{8}\)
(B) \(\frac{1}{3}\)
(C) \(\frac{3}{8}\)
(D) \(\frac{5}{8}\)
(E) \(\frac{2}{3}\)
(A) \(\frac{1}{8}\)
(B) \(\frac{1}{3}\)
(C) \(\frac{3}{8}\)
(D) \(\frac{5}{8}\)
(E) \(\frac{2}{3}\)
Re: A certain coin with heads on one side and tails on the other
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31 Jul 2018, 07:19
31 Jul 2018, 07:19
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It could be T H T, H T T or T T H
In each of the case the probability would be \(\frac{1}{2} * \frac{1}{2} * \frac{1}{2} = \frac{1}{8}\)
For 3 instances it would be \(\frac{3}{8}\)
In each of the case the probability would be \(\frac{1}{2} * \frac{1}{2} * \frac{1}{2} = \frac{1}{8}\)
For 3 instances it would be \(\frac{3}{8}\)
Re: A certain coin with heads on one side and tails on the other
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09 Aug 2018, 14:29
09 Aug 2018, 14:29
Expert Reply
Explanation
There are only 2 possible outcomes for each flip and only 3 flips total. The most straightforward approach is to list all of the possible outcomes: {HHH, HHT, HTH, HTT, TTT, TTH
THH, THT}.
Of these 8 possibilities, 3 of the outcomes have one head and two tails, so the probability of this event is \(\frac{3}{8}\).
Alternatively, count the total number of ways of getting 1 head without listing all the possibilities. If the coin is flipped 3 times and you want only 1 head, then there are 3 possible positions for the single head: on the first flip alone, on the second flip alone, or on the third flip alone. Since there are 2 possible outcomes for each flip, heads or tails, there are (2)(2)(2) = 8 total outcomes. Again, the probability is \(\frac{3}{8}\).
There are only 2 possible outcomes for each flip and only 3 flips total. The most straightforward approach is to list all of the possible outcomes: {HHH, HHT, HTH, HTT, TTT, TTH
THH, THT}.
Of these 8 possibilities, 3 of the outcomes have one head and two tails, so the probability of this event is \(\frac{3}{8}\).
Alternatively, count the total number of ways of getting 1 head without listing all the possibilities. If the coin is flipped 3 times and you want only 1 head, then there are 3 possible positions for the single head: on the first flip alone, on the second flip alone, or on the third flip alone. Since there are 2 possible outcomes for each flip, heads or tails, there are (2)(2)(2) = 8 total outcomes. Again, the probability is \(\frac{3}{8}\).
