Problem Solving

tvtt2010 wrote:on a certain road 10% of the mototorist exceed the posted limit and receive speeding tickets, but 20% of the motorists who exceed the posted speedlimit do not receive speeding ticket. What percent of the motorists on the road exceed the posted speed limit?
A) 10,5%
B) 12,5%
C) 15%
D) 22%
E) 30%

Thanks

tvtt2010 wrote:on a certain road 10% of the mototorist exceed the posted limit and receive speeding tickets, but 20% of the motorists who exceed the posted speedlimit do not receive speeding ticket. What percent of the motorists on the road exceed the posted speed limit?
A) 10,5%
B) 12,5%
C) 15%
D) 22%
E) 30%

Let us use the following representations:

Let E= The event of exceeding the speed limit.
E'= The event of not exceeding the speed limit.
T = The event of receiving tickets
T'= TThe event of not receiving tickets
Given:
P(E n T)= 0.1 [read as 'probability of E intersection T' ]
P(T'/E)= 0.2 [read as 'probability of T' given E']
Since P( T'/E) + P(T/E) = 1
= 0.2 + P(T/E) = 1
Therefore, P(T/E) =0.8

Required: P(E)=?
Now you can use the conditional rule of probability:
P(T/E) = P(T n E)/ P(E)
0.8 = 0.1/ P(E)
P(E)= 0.1/0.8
= 0.125
= 12.5%
Hope this helps.






Thanks

GMATGuruNY wrote:

tvtt2010 wrote:on a certain road 10% of the mototorist exceed the posted limit and receive speeding tickets, but 20% of the motorists who exceed the posted speedlimit do not receive speeding ticket. What percent of the motorists on the road exceed the posted speed limit?
A) 10,5%
B) 12,5%
C) 15%
D) 22%
E) 30%

Thanks

Let motorists who exceed the speed limit = 10.
Motorists who don't receive a ticket = .2*10 = 2.
Thus, motorists who receive a ticket = 10-2 = 8.
Since the 8 motorists who receive a ticket are 10% of the total, total = 80. (8 is 10% of 80.)
Motors who exceed the speed limit/Total = 10/80 = 12.5%.

BY wrote:

GMATGuruNY wrote:

tvtt2010 wrote:on a certain road 10% of the mototorist exceed the posted limit and receive speeding tickets, but 20% of the motorists who exceed the posted speedlimit do not receive speeding ticket. What percent of the motorists on the road exceed the posted speed limit?
A) 10,5%
B) 12,5%
C) 15%
D) 22%
E) 30%

Thanks

Let motorists who exceed the speed limit = 10.
Motorists who don't receive a ticket = .2*10 = 2.
Thus, motorists who receive a ticket = 10-2 = 8.
Since the 8 motorists who receive a ticket are 10% of the total, total = 80. (8 is 10% of 80.)
Motors who exceed the speed limit/Total = 10/80 = 12.5%.

Thanks for the explanation Guru!

But i have some confusion in the first sentence of the Qs.

10% of the mototorist exceed the posted limit and receive speeding tickets

say there are total 100 motorist.

10 exceed the posted limit and receive the ticket (as well).

Does the sentence mean : 10 % of the motorist exceed the posted limit and some of them receive speeding tickets.[/b][/u]