A tyre manufacturing company kept a record of the distance covered before a tyre needed to be placed . The table given below shows the results of 1000 cases .

If you buy a tyre of this company , what is the probability that
(i) it will need to be replaced before it has covered 4000 km ?
(ii) It will last more than 9000 km ?
(iii) it will need to be replaced after it has covered somewhere between 4000 km and 14000 km ?

Explanation

Total number of cases = 1000 .
(i) Let `E_(1)` be the event that a tyre will need to be replaced before covering 4000 km .
Number of tyres to be replaced before covering 4000 km = 20 .
`therefore P (E_(1)) = (20)/(1000) = 0.02`
(ii) Let `E_(2)` be the event that a tyre will last more than 9000 km .
Number of tyres that will last more than 9000 km
`= 325 + 445 = 770`.
`therefore P(E_(2)) = (770)/(1000) = 0.77`.
(iii) Let `E_(3)` be the event that a tyre needs replacement between 4000 km and 14000 km .
Number of tyre which need replacement after covering between 4000 km and 14000 km = 210 + 325 = 535
`therefore P(E_(3)) = (535)/(1000) = 0.535`.