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# A pyramid of 12 playing cards is such a state that if any individual

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Math Expert
Joined: 02 Sep 2009
Posts: 58410
A pyramid of 12 playing cards is such a state that if any individual  [#permalink]

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02 Oct 2018, 02:36
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Difficulty:

55% (hard)

Question Stats:

54% (01:24) correct 46% (01:22) wrong based on 89 sessions

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A pyramid of 12 playing cards is such a state that if any individual card falls, the entire pyramid collapses. If for each individual card, the probability of falling during time period of 1 minute is 0.05, what is the probability that the pyramid will collapse during time period of 1 minute?

(A) 0.05
(B) 0.05^12
(C) 1 − 0.95^12
(D) 0.95^12
(E) 1 − 0.05^12

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Re: A pyramid of 12 playing cards is such a state that if any individual  [#permalink]

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02 Oct 2018, 03:36
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Since for all cards the probability is same that is 0.05, and it is given that if any one card collapses then the whole pyramid will collapse.. so the probability of collapse of pyramid is 0.05.
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Joined: 16 Jan 2017
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Re: A pyramid of 12 playing cards is such a state that if any individual  [#permalink]

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05 Oct 2018, 01:07
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P(pyramid will fall)= 1-P(Pyramid won't fall)
Now, for P(Pyramid won't fall), no card can collapse.
So, P(Pyramid won't fall)= (1-0.05)*(1-0.05)*......12times
=0.95^12
therefore, P(pyramid will fall)= 1-(0.95^12)
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Re: A pyramid of 12 playing cards is such a state that if any individual  [#permalink]

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05 Oct 2018, 07:26
Is it not the same as this question: https://gmatclub.com/forum/a-string-of- ... 31205.html
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Re: A pyramid of 12 playing cards is such a state that if any individual  [#permalink]

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09 Oct 2018, 10:37
Bunuel wrote:
A pyramid of 12 playing cards is such a state that if any individual card falls, the entire pyramid collapses. If for each individual card, the probability of falling during time period of 1 minute is 0.05, what is the probability that the pyramid will collapse during time period of 1 minute?

(A) 0.05
(B) 0.05^12
(C) 1 − 0.95^12
(D) 0.95^12
(E) 1 − 0.05^12

Since the probability that a card will fall is 0.05, we see that the probability that a card will NOT fall is 1 - 0.05 = 0.95.

This question is asking the probability that the pyramid collapses (i.e., that at least one card falls) in the 1-minute time period..We can use the formula 1 - P(no card falls) = P(at least one card falls).

P(no card falls) = 0.95^12, so P(at least one card falls) is 1 - 0.95^12.

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Re: A pyramid of 12 playing cards is such a state that if any individual   [#permalink] 09 Oct 2018, 10:37
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