.    The following table gives distance (in km) that 40 engineers have to travel from their residences to their work places:-
 
  Distance (in km) 0 - 5 5 - 10 10 - 15 15 - 20 20 - 25 25 - 30 30 - 35 No of engineers 5 11 11 9 1 1 2  
Find the probability that an engineer selected at random lives at a distance of:-
(i) 10 – 15 km (event E1)  (ii) more than 35 km (event E2)       (iii) less than 10 km (event E3)        (iv) upto 35 km

answers in step please

Dear Student,

Please find below the solution to the asked query:

We have the following table gives distance (in km) that 40 engineers have to travel from their residences to their work places:
 
Distance (in km) 0 - 5 5 - 10 10 - 15 15 - 20 20 - 25 25 - 30 30 - 35
No. of engineers 5 11 11 9 1 1 2

We know : Probability P ( E )  = Total number of desired events n ( E )Total number of events n ( S )

Here ,

n ( S ) = 40

i ) 10 - 15 km ( event E1 )  ,  From given table we get 

n ( E1 ) = 11

Therefore,

Probability that an engineer selected at random lives at a distance of ( 10 - 15 km ) = 1140                             ( Ans )

ii ) more than 35 km ( event E2 )  ,  From given table we get 

n ( E2 ) = 0

Therefore,

Probability that an engineer selected at random lives at a distance of ( more than 35 km ) = 040 = 0                             ( Ans )     iii ) less than 10 km (event E3)  ,  From given table we get 

n ( E3 ) = 5 +  11 =  16

Therefore,

Probability that an engineer selected at random lives at a distance of ( less than 10 km ) = 1640 = 25                             ( Ans )  iv ) Upto 35 km ,  From given table we get 

n ( E4 ) = 5 + 11 + 11 + 9 + 1 + 1 + 2 =  40

Therefore,

Probability that an engineer selected at random lives at a distance of ( upto 35 km ) = 4040 = 1                             ( Ans ) 
Hope this information will clear your doubts about topic.

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