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The probability is 1/2 that a certain coin will turn up

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The probability is 1/2 that a certain coin will turn up  [#permalink]

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New post 17 Nov 2013, 18:39
1
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

70% (00:56) correct 30% (01:10) wrong based on 79 sessions

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The probability is 1/2 that a certain coin will turn up heads on any given toss. If the coin is to be tossed four times, what is the probability that on at least one of the tosses the coin will turn up tails?

(A) 1/16
(B) 1/8
(C) 1/2
(D) 7/8
(E) 15/16


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Re: The probability is 1/2 that a certain coin will turn up  [#permalink]

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New post 17 Nov 2013, 21:44
avohden 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 four times, what is the probability that on at least one of the tosses the coin will turn up tails?

(A) 1/16
(B) 1/8
(C) 1/2
(D) 7/8
(E) 15/16


Image


It is easier to find the probability that on the 4 tosses, there will be no tails.

P(at least one tails) = 1 - P(No tails)

P(No tails) = P(All 4 Heads) = (1/2)*(1/2)*(1/2)*(1/2) = 1/16

P(at least one tails) = 1 - 1/16 = 15/16
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Re: The probability is 1/2 that a certain coin will turn up  [#permalink]

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New post 17 Nov 2013, 23:44
avohden 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 four times, what is the probability that on at least one of the tosses the coin will turn up tails?

(A) 1/16
(B) 1/8
(C) 1/2
(D) 7/8
(E) 15/16


Image


"Stolen" OG question:
Quote:
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


Discussed here: the-probability-is-1-2-that-a-certain-coin-will-turn-up-head-144730.html
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Senior Manager
Senior Manager
User avatar
Status: 1,750 Q's attempted and counting
Affiliations: University of Florida
Joined: 09 Jul 2013
Posts: 492
Location: United States (FL)
Schools: UFL (A)
GMAT 1: 600 Q45 V29
GMAT 2: 590 Q35 V35
GMAT 3: 570 Q42 V28
GMAT 4: 610 Q44 V30
GPA: 3.45
WE: Accounting (Accounting)
Re: The probability is 1/2 that a certain coin will turn up  [#permalink]

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New post 19 Nov 2013, 21:24

Official Explanation


Answer: E
- It's easier to solve for the opposite of what the question is asking for when you see the term "at least." The opposite of at least one tail is no heads. The only way zero heads will result is if each of the four flips results in a tail:

p = (1/2)(1/2)(1/2)(1/2) = 1/16

That's the opposite of the answer, so subtract it from 1:

p = 1 - 1/16=15/16,choice (E).
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New post 09 Mar 2019, 12:45
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Re: The probability is 1/2 that a certain coin will turn up   [#permalink] 09 Mar 2019, 12:45
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