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

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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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 probability that- 

(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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