Question

The figure shows a one-way road network system from Town P to Towns R, S and T. Any car leaving Town P will pass through either Tunnel A or Tunnel B and arrive at Towns R, S and T via the roundabout Q. A survey shows that 2/5 of the cars leaving P will pass through Tunnel A. The survey also shows that 1/7 of all the cars passing through the roundabout Q will arrive at R, 2/7 at S and 4/7 at T.
(a) Two cars leave P. Find the probabilities that:
(i) one of them arrives at R and the other one at S,
(ii) both of them arrive at S, one through Tunnel A and the other one through Tunnel B.

Answer 1

@phi @ganeshie8

Answer 2

a)one of them arrives at R and the other one at S,
p(R)*p(S)+p(S)*P(R)
1/7 *2/7+2/7*1/7=4/49

Answer 3

does it also include the tunnels?

Answer 4

hmmm let me check again

Answer 5

sry i guess im wrong ,
u shud check all the possiple tunnels too

Answer 6

the book's answer is 4/49. But i don't know is it necessary to calculate the tunnels or not..

Answer 7

why we don't need to calculate the tunnels?

Answer 8

i guess its not necessary , but u need to check from somone else

Answer 9

ok, and part b?

Answer 10

the tunnels do not matter... it is 100% chance that you go from P to Q
if you don't care how you get to Q, the tunnels do not matter.

Answer 11

@phi oh i see...

Answer 12

hmm this is wat i cud think of:o
ok so they arrive P
p(A)p(s)*P(B)P(S)+P(B)P(S)*p(A)p(s)
(2/5*2/7)*(1/5*2/7)+(1/5*2/7)+(2/5*2/7)=16/1225

Answer 13

for (b), there are 4 ways: AA, AB, BA, BB
to get to Q
and then 4/49 chance from Q to SS

Answer 14

@ikram002p i also do it like your way, but the answer is not 16/1225...
@phi yes....

Answer 15

aha ic hmm wats te correct answer :o

Answer 16

ikram should use 2/5 and 3/5 (not 1/5

Answer 17

ops!

Answer 18

@ikram002p @phi oh i got it now, i also made the same mistake from @ikram002p .... the answer is 48/1225?

Answer 19

yes, that is what I got 48/1225

Answer 20

hmm so this is how we got the answer ?
p(A)p(s)*P(B)P(S)+P(B)P(S)*p(A)p(s)
(2/5*2/7)*(3/5*2/7)+(3/5*2/7)+(2/5*2/7)=48/1225

Answer 21

@ikram002p yes.

Answer 22

@phi @ikram002p thank you both :D

Answer 23

np :)
im not good in this lol

Answer 24

@ikram002p haha i still have another questions ...