IIT JEE , AIEEE Forum - Mathematics , Algebra

raman_shadow

in a game of tennis, A can return the ball legally 3 out of 4 times and B can return the ball 4 out of 5 times. Concidering service to be always legal, find the probability that

1. A wins

2. the ball is dead after 4 legal returns excluding the service

if B serves 1st in both cases

iam_quantized

A CAN WIN IN HIS 1ST,2ND ......SHOTS SO

PROB A WINS IS = (3/4)(1/5) + (3/4)(4/5)(3/4)(1/5) + (3/4)(4/5)(3/4)(4/5)(3/4)1/5) +..................... CLEARLY ITS AN INFINE GP WITH 1ST TERM (3/4)(1/5) AND CR 3/5... ANS TO PART A IS 3/8.

FOR B PART CONSIDER THE SAME SEQUENCE BUT ONLY 1ST 2 TERMS

Asmita

Please will u make this sol. more clear 2 me so that I can understand it.But still I've given a salute 4 ur efforts.

iam_quantized

THE FIRST TERM IN THE SEQUENCE IS p THT A RETURNS THE BALL SUCCESSFULLLY AND B MISSES IT SO (3/4)(1/5)...THE NEXT TERM IS A RETURNS SUCC. AND B RETURNS SUCC. AND A AGAIN RETURNS SUCC AND B MISSES IT....SO (3/4)(4/5)(3/4)(1/5)...AND SO ON UPTO INFINITY......

FOR SECOND PART ONLY 4 RETURNS R TO BE CONSIDERED SO 1ST 2 TERMS OF THE SEQUENCE COUNTS.

GOT IT!!!!!!

Asmita

Thanks a lot !!!

iam_quantized

ur welcome...hey iam new 2 goiit can u pls help me...

krishna.gopal

Right answer by Mr. Quantized. In such games solution comes by making infinite GP

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