## mr.luna 3 years ago Suppose while playing tennis, Venus gets her first serve in 75% of the time. when she gets her first serve in, she wins a point 80% of the time...

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1. mr.luna

if she misses her first serve, her second serve goes in 90% of the time. whe this happens, she wins the point on her second serve 35% of the time. find the probability that venus wins a point when she is serving.

2. alexandercpark

probability was never my strong point, but I could take a guess at this.

3. mr.luna

you guys have any ideas of how to go about solving this?

4. RaphaelFilgueiras

\[p(wp)=p(wp|Gs1).P(Gs1)+p(wp|Gs2).P(Gs2)\]

5. alexandercpark

what i would do would be: \[.75*.80 + (1 - .75*.80)*.9*.35\] the first part being the probability of her winning her first serve and the second of her winning her second serve given a result of her first serve. again its been forever since I've done any probability

6. RaphaelFilgueiras

p(wp|Gs1)=80% p(wp|Gs2)=35% p(Gs1)=75% P(Gs2)=90%

7. mr.luna

is the periods in between multiplications symbols? @RaphaelFilgueiras

8. RaphaelFilgueiras

tihs is the probability of win a point if she gets first server

9. mr.luna

a player is allowed two serves each time in tennis. sorry i forgot to mention that.

10. RaphaelFilgueiras

the secons time Gs2

11. RaphaelFilgueiras

P(wp) is the probability to win a pint

12. mr.luna

the question just says find the P when she is serving. it doesnt when wether is first or second. what shoudl i do?

13. RaphaelFilgueiras

that formula take accounting the two cases,its impossible she gain a ponit without serving

14. alexandercpark

have you played tennis before?

15. alexandercpark

or know how the serving works?

16. mr.luna

oh ok. the problem also says draw a tree diagram. i will post here.

17. mr.luna

nope.

18. alexandercpark

in tennis you have two attempts to get in a good serve with each serve. IF you miss the first one you move onto the second.

19. mr.luna

|dw:1334986543479:dw|

20. alexandercpark

|dw:1334997467614:dw|

21. alexandercpark

try mulitplying the circled numbers together, then the squared ones, then adding them together,.

22. mr.luna

ok, that makes alot more sense. thanks for help! really aprreciate it

23. mr.luna

i got 67.8%

24. amogh

So, i) She could either get her first serve in and get a point (0.75 * 0.80) ii) She could else get her first serve wrong, second serve right and point on her second serve ( 0.25 * 0.90 * 0.35) Sum up i) and ii) 0.6 + 0.079 That's 67.9% , same as what you got! So guess its right! :D