Question

In an experiment Tom drops 12 drawing pins onto a hard floor. He does the experiment 10 times and counts how many pins land 'point up'. His results were as follows.

a) use Tom's data to work out the probability that a single drawing pin will land point up.
b) Tom continues the experiment until he has dropped the 12 drawing pins 100 times. About how many drawing pins in total would you expect to land point up? ​

Answer 1

a) 0.35

b) 420 drawing pins

Explanation:

a) The question relates to the relative frequency of the pins pointing up which is found by the formula as follows;

`Relative \ frequency = (Number \ of \ successful \ trials )/(Total \ number \ of \ trials)`

The total number of pins land 'point up' = 3 + 5 + 6 + 2 + 4 + 7 + 3 + 3 + 4 + 5

The total number of pins land 'point up' = 42 successful trials

Total number of trials = 12 × 10 = 120 trials

`Relative \ frequency = (42 )/(120)= (7)/(20)`

Due to the large number of trials, the relative frequency ≈ Probability and the probability that a single pin will land point up = 7/20 = 0.35

b) Given that the number of trials now = 12 × 100 = 1200, we have;

The expected number of drawing pins in total that would land point up = 0.35×1200 = 420 pins.