- #1

WMDhamnekar

MHB

- 378

- 28

Hi,

What is your probability of winning a game of tennis, starting from the even score Deuce (40-40), if your probability of winning each point is 0.3 and your opponent’s is 0.7?

My answer:

I think the sequence of independent trials are required to win a game of tennis starting from even score Deuce(40-40),each of which is a success with probability (0.3 × 0.3 =0.09) or a failure with probability (0.7 × 0.3 + 0.7 × 0.3 =0.42). Suppose, the independent trials to win a game of tennis are

$$ \displaystyle\sum_{n=0}^{\infty} 0.09 \cdot (0.42)^n =\lim_{n \to \infty}\frac{0.09\cdot ( 1 - 0.42^n)}{1- 0.42}= 0.15517 $$ = 15.51 %

What is your probability of winning a game of tennis, starting from the even score Deuce (40-40), if your probability of winning each point is 0.3 and your opponent’s is 0.7?

My answer:

I think the sequence of independent trials are required to win a game of tennis starting from even score Deuce(40-40),each of which is a success with probability (0.3 × 0.3 =0.09) or a failure with probability (0.7 × 0.3 + 0.7 × 0.3 =0.42). Suppose, the independent trials to win a game of tennis are

**n**. That means after**(n-1)**trials of failures, the nth trial is success.$$ \displaystyle\sum_{n=0}^{\infty} 0.09 \cdot (0.42)^n =\lim_{n \to \infty}\frac{0.09\cdot ( 1 - 0.42^n)}{1- 0.42}= 0.15517 $$ = 15.51 %

Last edited: