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Question: Two person A and B agree to meet at a place between 5 to 6 pm. The first one to arrive waits for 20 ...

Two person A and B agree to meet at a place between 5 to 6 pm. The first one to arrive waits for 20 minute and then leave. If the time of their arrival be independent and at random then the probability that A & B meet is -

A

1/3

B

4/9

C

5/9

D

2/3

Answer

5/9

Explanation

Solution

A and B arrives at the place of the meeting 'a' minute and 'b' minute after 5 P.M. Their meeting is possible only if |a – b| £ 20.

0 £ a £ 60 and 0 £ b £ 60– 20 £ a – b £ 20

– 20 £ x – y £ 20 Ž y £ x + 20 and y ³ x – 20

Required probability=

= Ar⁡(OPQR)−2Ar(ΔAPB)Ar⁡(OPQR)\frac { \operatorname { Ar } ( \mathrm { OPQR } ) - 2 \mathrm { Ar } ( \Delta \mathrm { APB } ) } { \operatorname { Ar } ( \mathrm { OPQR } ) }

= [60×60−22×40×40]60×60\frac { \left[ 60 \times 60 - \frac { 2 } { 2 } \times 40 \times 40 \right] } { 60 \times 60 } = 5/9