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03 Jan 2019, 09:18
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
78% (01:20) correct
22%
(01:54)
wrong
based on 154
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A coin with heads on one side and tails on the other has a 1/2 probability of landing on heads. If the coin is flipped 5 times, how many distinct outcomes are possible if the last flip must be heads? Outcomes are distinct if they do not contain exactly the same results in exactly the same order.
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
03 Jan 2019, 09:47
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Bunuel
Take the task of listing possible outcomes and break it into stages.
Stage 1: Select an outcome for the 1st flip
The flip can be heads or tails.
So, we can complete stage 1 in 2 ways
Stage 2: Select an outcome for the 2nd flip
The flip can be heads or tails.
So, we can complete stage 2 in 2 ways
Stage 3: Select an outcome for the 3rd flip
We can complete this stage in 2 ways
Stage 4: Select an outcome for the 4th flip
We can complete this stage in 2 ways
Stage 5: Select an outcome for the LAST flip
This flip MUST be heads.
So, we can complete this stage in 1 way
By the Fundamental Counting Principle (FCP), we can complete all 6 stages (and thus list possible outcomes) in (2)(2)(2)(2)(1) ways (= 16 ways)
Answer: E
Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.
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03 Jan 2019, 10:04
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Bunuel
We need 5 flips of a fair coin such that
__ __ __ __ H
On each of the previous flips, we can have either Heads or Tails so there are 2 ways.
For the 4 previous flips then, there are 2*2*2*2 = 16 ways
Answer (E)
