A tyre company records distances before replacement in 1000 cases. Class 9

A tyre company records distances before replacement in 1000 cases. Class 9

Question 1.

A tyre company records distances before replacement in 1000 cases. Class 9

Find the probability that a randomly chosen tyre lasts:

i. Less than 4000 km.

ii. Between 4000 and 14000 km.

iii. More than 14000 km.

Solution:

i. Total number of outcomes = 1000

Number of favourable outcomes for less than 4000 km = 20

∴ P(less than 4000 km)

$=\frac{\text { Number of favourable outcomes }}{\text { Total number of outcomes }}=\frac{20}{1000}=0.02$

∴ The probability that tyre lasts less than 4000 km is 0.02.

ii. Number of favourable outcomes for between 4000 and 14000 km = 210 + 235 = 535

P(Between 4000 and 14000 km)

$\begin{aligned} & =\frac{\text { Number of favourable outcomes }}{\text { Total number of outcomes }} \\ & =\frac{535}{1000}=0.535\end{aligned}$

∴ The probability that tyre lasts between 4000 and 14000 is 0.535

iii. Number of favourable outcomes for more than 14000 km = 445

∴ P(more than 14000 km)

$=\frac{\text { Number of favourable outcomes }}{\text { Total number of outcomes }}=\frac{445}{1000}=0.445$

∴ The probability that tyre lasts more than 14000 km is 0.445.