If one of the challenges is randomly selected, find the probability that: a. It was rejected b. It was made by a male player or was rejected c. It was rejected given it was made by a male player d. It was made by a female player give it was accepted
Chapter 4 Collected Assignment
For questions 1 and 2, use the following results from the 839 player challenges to referee calls in the first US Open tennis tournament to use the Hawk-Eye electronic instant replay system.
|
|
Player Challenge was Accepted |
Player Challenge was Rejected |
|
Male Player |
201 |
288 |
|
Female Player |
126 |
224 |
1. If one of the challenges is randomly selected, find the probability that:
a. It was rejected
b. It was made by a male player or was rejected
c. It was rejected given it was made by a male player
d. It was made by a female player give it was accepted
2. If three challenges are randomly selected, find the probability that:
a. They were all made by a female player
i. With replacement
ii.Without replacement
b. At least one was made by a female player
3. How many ways can a team captain and co-captain be chosen on a team of 16 players?
4. How many ways can a group of 4 players on a team of 16 be chosen to plan and organize a team training?
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For questions 1 and 2, use the following results from the 839 player challenges to referee calls in the first US Open tennis tournament to use the Hawk-Eye electronic instant replay system.
|
|
Player Challenge was Accepted |
Player Challenge was Rejected |
|
Male Player |
201 |
288 |
|
Female Player |
126 |
224 |
1) One of the challenges is randomly selected, then the
(a) The probability that the randomly selected challenges was Rejected,
P( Rejected) = n(rejected)/Total player
= 512/839 = 0.61025029797 ~ 0.61025
(b) The probability that the randomly selected challenges was made by a male player or was rejected is,
P( Male or Rejected) = P(Male) + P(Rejected) - P(Male and Rejected)
= (489/839) + (512/839) - (288/839)
= 713/839 = 0.84982
(c) The probability that the randomly selected challenges was rejected given it was made by a male player is , P( Rejected | Male) = n( Rejected and male)/n(male)
= 288/489 = 0.58896
(d) The probability that the randomly selected challenges was made by a female player give it was accepted is , P(Female | Accepted)
= n(Female and Accepted)/n(Accepted)
= 126/327 = 0.38532
2. If three challenges are randomly selected, find the probability that:
a. They were all made by a female player
i. With replacement
ii.Without replacement
b. At least one was made by a female player
3. How many ways can a team captain and co-captain be chosen on a team of 16 players?
4. How many ways can a group of 4 players on a team of 16 be chosen to plan and organize a team training?
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