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

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

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New post 30 Jun 2017, 06:19
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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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The probability that a train arrives late at a particular station is 2  [#permalink]

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New post 30 Jun 2017, 08:29
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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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New post 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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New post 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.

Answer: C
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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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