If At First... Statistics In Your World 
Student Notes
Teachers Notes
The Minibus
 
Which Key?
 
Traffic Lights
 

More Simulations
For these simulations use the random number table on page R4.

The numbers are printed in pairs, but you can read them one at a time.
28 37 49 86 gives 2 8 3 7 4 9 8 6.

The Minibus
You will need page R1.

Albert Ward decides to run his minibus on a Saturday.

On Saturdays out of every 8 people who book 7 come.

Here we need the digits 1,2,3,4,5,6,7,8

If the number is 1, the person does not come.
If the number is 2,3,4,5,6,7,8, the person does come.
If the number is 9, 0, we go to the next number.

a Carry out this simulation for five trips. Record your results on Table 4 of page R1.
b How many times were there too many passengers?
c How many times was there one empty seat?
d How many times were there two or more empty seats?

Discuss your results with a friend.

Which Key?
You will need page R3.

A man has six keys in his pocket. He returns home late one night when it is very dark. He takes a key to open the door. If it is the wrong key, he drops it back into his pocket and picks out another. (It could be the same one!)

How many, keys does he need to try?

You can simulate this using random numbers from 1 to 6.

If the number is 1, it is the correct key and the trial is complete.

If the number is 2, 3, 4, 5, 6, it is the wrong key and he must try again.

Ignore numbers 7,8,9, and 0.
In a simulation 6, 4, 5, 1, he needed to try four times.

a Carry out this simulation five times. Record the results of each trial in Table 5 on page R3. Find the mean of the five trials.

Another night the man thinks more carefully. If a key does not fit, he takes a different one before putting the last key back into his pocket.

For this simulation you must not use a number if it is the same as the one before.

b Do this five times. Record the results of each trial on Table 6 on Page R3. Find the mean of the five trials.

The next time the man thinks very carefully. If the key does not fit, he puts it back into another pocket. This time a random number cannot be repeated at all so, at most, he tries all six keys.

c Do this five times. Record the results of each trial in Table 7 on page R3. Find the mean of the five trials.
d Which of the three ways is the fastest? Which is the slowest?

Is this what you would expect?

Traffic Lights
You will need page R3.

Fred passes through two sets of traffic lights each morning. He has timed both of them. He finds that the first set shows green for 30 seconds out of 50 seconds.

a What is the probability that Fred does not stop at the first set of traffic lights?

Write out a method, as in B3, for simulating this probability using random numbers.

The second set of traffic lights shows green for 30 seconds out of 90 seconds.

b What is the probability that Fred does not stop at the second set of traffic lights?
c Write out a method for simulating this probability using random numbers.

To simulate Fred's journey through both sets of traffic lights you must choose two random numbers.

Use the first one to decide whether Fred stops at the first set of lights.

Use the second one to decide whether Fred stops at the second set of lights.

d Do this simulation 20 times. Enter your results in Table 8 on Page R3.
e How many times did Fred have to stop at:
both sets of lights,
only one set of lights,
neither set of lights?
f Use the results from c to estimate the probability that:
Fred will stop at both sets of traffic lights.
Fred stops at only one set of traffic lights.
Fred will not have to stop at all.

 

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