QUESTION 7
Easy
A tyre company records distances before replacement in 1000 cases.
| Distance (km) | Less than 4000 | 4001 to 9000 | 9001 to 14000 | More than 14000 |
|---|---|---|---|---|
| Number of cases | 20 | 210 | 325 | 445 |
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
1
Note down given data
Total number of tyres \( = 20 + 210 + 325 + 445 = 1000\)
So, total outcomes, \(n(S) = 1000\)
So, total outcomes, \(n(S) = 1000\)
2
(i) Probability that a tyre lasts less than 4000 km
Number of tyres lasting less than 4000 km \( = 20\)
\(P(less\,than\,4000) = \frac{20}{1000} = \frac{1}{50}\)
So, the probability that a randomly chosen tyre lasts less than 4000 km is \(\frac{1}{50}\).
\(P(less\,than\,4000) = \frac{20}{1000} = \frac{1}{50}\)
So, the probability that a randomly chosen tyre lasts less than 4000 km is \(\frac{1}{50}\).
3
(ii) Probability that a tyre lasts between 4000 km and 14000 km
Tyres lasting between 4000 km and 14000 km are in the groups:
(i) 4001 to 9000 km = 210
(ii) 9001 to 14000 km = 325
So, total favourable outcomes \(= 210 + 325 = 535\)
\(P(4000\,km \,to \,14000 km) = \frac{535}{1000} = \frac{107}{200}\) The probability that a randomly chosen tyre lasts between 4000 km and 14000 km is \(\frac{107}{1000}\).
(i) 4001 to 9000 km = 210
(ii) 9001 to 14000 km = 325
So, total favourable outcomes \(= 210 + 325 = 535\)
\(P(4000\,km \,to \,14000 km) = \frac{535}{1000} = \frac{107}{200}\) The probability that a randomly chosen tyre lasts between 4000 km and 14000 km is \(\frac{107}{1000}\).
4
(iii) Probability that a tyre lasts more than 14000 km
Number of tyres lasting more than 14000 km \(= 445\)
So, \(P(more\, than \,14000 \,km) = \frac{445}{1000} = \frac{89}{200}\)
The probability that a randomly chosen tyre lasts more than 14000 km is \(\frac{89}{200}\).
So, \(P(more\, than \,14000 \,km) = \frac{445}{1000} = \frac{89}{200}\)
The probability that a randomly chosen tyre lasts more than 14000 km is \(\frac{89}{200}\).
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Final Answer :
(i) P(less than 4000 km) = \(\frac{1}{50}\)
(ii) P(4000 to 14000 km) = \(\frac{107}{200}\)
(iii) P(more than 14000 km) = \(\frac{89}{200}\)
Concept Note
In experimental probability, probability is based on observed data rather than theoretical outcomes.
Experimental probability =\(\frac{Number\,of\,times\,the\,event\,occured}{Total\,number\,of\,trials}\)