P3 | Maths Made Easy

P3

QUESTION: Arthur recorded vehicles passing his house and noted if they were a car or not, and if they were black or not, in the adjacent table. He claims, “if a vehicle passes my house, there is exactly a 50% chance it will be car that is not black”. Comment, with justification, on Arthur’s claim.

 

ANSWER: To work out the probability of a random vehicle passing Arthur’s house, we need to find the relative frequency of not-black cars. Doing this, we get

\dfrac{\text{number of not-black cars}}{\text{total number of vehicles}}=\dfrac{56}{20+56+12+32}=\dfrac{7}{15}

Putting it into a calculator, we see that \dfrac{7}{15}=0.4666...=46.7\%. Given that 50\%=0.5, we can see that the relative frequency of not-black cars is close to 50\% but not exactly 50\%, therefore Arthur is not correct.