A tyre manufacturing company kept a record of the distance covered before a tyre to be replaced. Following table shows the results of 1000 cases. Distance in km:             Less tan 400                                      400 to 900  900 to 1400                          More than 1400 Number of tyres:           210             325                                      385             80 If you boy a tyre of this company, what is the probability that: (i)               it will need to be replaced before it has covered 400 km? (ii)             it will last more than 900 km? (iii)           it will need to be replaced after it has covered somewhere between 400 km and 1400 km? (iv)           it will not need to be replaced at all? (v)             it will need to be replaced?

Explanation

(i)`20` tyres need to be replaced before `4000` km out of `1000` tyres.
Probability that the tyre needs to be replaced before covering `4000 km = 20/1000 = 0.02` or `2%`
(ii) tyres replaced after `9000` km = `325+445 = 770` tyres out of `1000`
probability = `770/1000 = 0.77 `or `77%`
(iii) tyres replaced between `4000` and `14000 km = 325+210+20 = 555` tyres out of `1000`
probability = `555/1000 = 0.555` or `55.5%`.