GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
A certain coin with heads on one side and tails on the other
[#permalink]
30 Jul 2018, 10:56
30 Jul 2018, 10:56
2
Expert Reply
1
Bookmarks
00:00
Question Stats:
82% (00:49) correct
17% (00:47) wrong based on 93 sessions
Hide Show timer Statistics
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
[#permalink]
31 Jul 2018, 07:19
31 Jul 2018, 07:19
2
1
Bookmarks
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
[#permalink]
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 \(\frac{3}{8}\).
