# Train station Probability help

• prime-factor
In summary, the probability of at least 8 out of 10 trains arriving on time at Roma Street station is 0.6778. To find the probability of at least 8 trains arriving on time for 9 out of the next 10 days, the values of n, x, p, and q must be adjusted accordingly, resulting in a probability of 0.09728.
prime-factor

## Homework Statement

Eighty per cent of all scheduled trains through
Roma Street station arrive on time. If 10 trains
go through the station every day, find:
a the probability that at least 8 trains are
on time
b the probability that at least 8 trains are
on time for 9 out of the next 10 days.

## Homework Equations

P(X = x) = nCxpxqn − x

## The Attempt at a Solution

P(X>=8)

n=10

x=8+9+10

p=0.8

q=0.2

P(X=8)+p(X=9)+p(X=10) = 0.6778

10C80.880.22 +10C90.890.21+10C100.8100.20

b I guess I would use:

P(X=8)+p(X=9)+p(X=10) = 0.6778

worked it out:

set:

n=10

x=9

p= 0.6778

q=0.3222

And I get: 0.09728

## 1. What is the "Train station Probability" problem?

The "Train station Probability" problem is a classic probability problem which involves predicting the likelihood of a train arriving at a specific time based on historical data and other factors.

## 2. How do you calculate the probability of a train arriving on time?

To calculate the probability of a train arriving on time, you need to gather data on the train's historical arrival times and use statistical methods such as mean and standard deviation to determine the likelihood of the train arriving within a certain time frame. Other factors such as weather and train schedule may also need to be taken into account.

## 3. What is the importance of the "Train station Probability" problem?

The "Train station Probability" problem is important because it can help train companies and travelers make informed decisions about train schedules and arrival times. It also serves as a practical application of probability and can be used to improve train transportation systems.

## 4. Can the "Train station Probability" problem be applied to other modes of transportation?

Yes, the principles of the "Train station Probability" problem can be applied to other modes of transportation such as buses, planes, and even traffic flow. Any situation where arrival times can be predicted based on historical data and other factors can be solved using probability methods.

## 5. What are some challenges in solving the "Train station Probability" problem?

One of the main challenges in solving the "Train station Probability" problem is gathering accurate and comprehensive data on the train's arrival times and other factors. Other challenges may include dealing with unpredictable events such as delays or cancellations, and determining the appropriate statistical methods to use for calculating probabilities.

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