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# The probability that a train arrives late at a particular station is 2

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Manager
Joined: 03 Feb 2017
Posts: 74
Location: Australia
GMAT 1: 720 Q48 V40
The probability that a train arrives late at a particular station is 2  [#permalink]

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30 Jun 2017, 06:19
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Difficulty:

55% (hard)

Question Stats:

62% (02:15) correct 38% (02:04) wrong based on 54 sessions

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The probability that a train arrives late at a particular station is 25%. There are four trains scheduled to arrive at the station today. What is the probability that at least three of them will arrive later than the scheduled time?

A) $$\frac{1}{256}$$

B) $$\frac{5}{256}$$

C) $$\frac{13}{256}$$

D) $$\frac{20}{256}$$

E) $$\frac{255}{256}$$
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Joined: 02 Aug 2009
Posts: 7575
The probability that a train arrives late at a particular station is 2  [#permalink]

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30 Jun 2017, 08:29
1
danlew wrote:
The probability that a train arrives late at a particular station is 25%. There are four trains scheduled to arrive at the station today. What is the probability that at least three of them will arrive later than the scheduled time?

A) $$\frac{1}{256}$$

B) $$\frac{5}{256}$$

C) $$\frac{13}{256}$$

D) $$\frac{20}{256}$$

E) $$\frac{255}{256}$$

Hi,
Probability that a train is late = $$\frac{25}{100} =\frac{1}{4}$$, so prob of train reaching in time =1-1/4= $$\frac{3}{4}$$
atleast THREE means
1) all four..
$$(\frac{1}{4})^4=\frac{1}{256}$$
2) Only three..
$$\frac{1}{4}*\frac{1}{4}*\frac{1}{4}*\frac{3}{4}*4=\frac{12}{256}$$
multiplication by 4 is as the train coming in time can be any of the 4

total $$\frac{12+1}{256}=\frac{13}{256}$$

c
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Re: The probability that a train arrives late at a particular station is 2  [#permalink]

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30 Jun 2017, 17:11
danlew wrote:
The probability that a train arrives late at a particular station is 25%. There are four trains scheduled to arrive at the station today. What is the probability that at least three of them will arrive later than the scheduled time?

A) $$\frac{1}{256}$$

B) $$\frac{5}{256}$$

C) $$\frac{13}{256}$$

D) $$\frac{20}{256}$$

E) $$\frac{255}{256}$$

1. There are 4 ways of 3 trains coming late. Probability of 3 trains coming late and one train not coming late is (1/4*1/4*1/4*3/4)*4=12/256
2. Probability of 4 trains coming late is 1/4*1/4*1/4*1/4=1/256
3. Final probability is 13/256
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Re: The probability that a train arrives late at a particular station is 2  [#permalink]

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04 Jul 2017, 08:12
danlew wrote:
The probability that a train arrives late at a particular station is 25%. There are four trains scheduled to arrive at the station today. What is the probability that at least three of them will arrive later than the scheduled time?

A) $$\frac{1}{256}$$

B) $$\frac{5}{256}$$

C) $$\frac{13}{256}$$

D) $$\frac{20}{256}$$

E) $$\frac{255}{256}$$

We are given that the probability that a train arrives late is 1/4.

We need to determine the probability that at least 3 trains arrive late. That is, we need to determine the probability that exactly 3 trains arrive late or that all 4 trains arrive late.

Let’s start with 3 late trains and 1 on-time train (L = late and T = on time):

P(L-L-L-T) = 1/4 x 1/4 x 1/4 x 3/4 = 3/256

Since we can organize the 3 Ls and 1 T in 4!/3! = 4 ways, the total probability is actually 3/256 x 4 = 12/256.

Next we can determine the probability that all 4 trains arrive late:

P(L-L-L-L) = 1/4 x 1/4 x 1/4 x 1/4 = 1/256

Thus, the probability of at least 3 trains arriving late is 12/256 + 1/256 = 13/256.

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Re: The probability that a train arrives late at a particular station is 2   [#permalink] 04 Jul 2017, 08:12
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