According to a​ poll, about 12​%of adults in a country bet on professional sports. Data indicates that 45.9​% of the adult population in this country is male. Complete parts​ (a) through​ (e). ​(a) Are the events​ "male" and​ "bet on professional​ sports" mutually​ exclusive? Explain.   A. Yes. A person can be both male and bet on professional sports at the same time.   B. No. A person can be both male and bet on professional sports at the same time.   C. No. A person cannot be male and bet on professional sports at the same time.   D. Yes. A person cannot be both male and bet on professional sports at the same time. ​(b) Assuming that betting is independent of​ gender, compute the probability that an adult from this country selected at random is a male and bets on professional sports.   ​P(male and bets on professional ​sports)=nothing ​(Type an integer or decimal rounded to four decimal places as​ needed.)   ​(c) Using the result in part​ (b), compute the probability that an adult from this country selected at random is male or bets on professional sports.   ​P(male or bets on professional ​sports)=nothing ​(Type an integer or decimal rounded to four decimal places as​ needed.)   ​(d) The poll data indicated that 7.1​% of adults in this country are males and bet on professional sports. What does this indicate about the assumption in part​ (b)?   A. The assumption was correct and the events are independent.   B. The assumption was incorrect and the events are not independent. ​(e) How will the information in part​ (d) affect the probability you computed in part​ (c)? Select the correct choice below and fill in any answer boxes within your choice.   A. ​P(males or bets on professional ​sports)=nothing ​(Type an integer or decimal rounded to four decimal places as​ needed.)   B. This information does not affect the probability computed in part​ (c).

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According to a​ poll, about 12​%of adults in a country bet on professional sports. Data indicates that 45.9​% of the adult population in this country is male. Complete parts​ (a) through​ (e).
​(a) Are the events​ "male" and​ "bet on professional​ sports" mutually​ exclusive? Explain.
 
A.
Yes. A person can be both male and bet on professional sports at the same time.
 
B.
No. A person can be both male and bet on professional sports at the same time.
 
C.
No. A person cannot be male and bet on professional sports at the same time.
 
D.
Yes. A person cannot be both male and bet on professional sports at the same time.
​(b) Assuming that betting is independent of​ gender, compute the probability that an adult from this country selected at random is a male and bets on professional sports.
 
​P(male and bets on professional
​sports)=nothing
​(Type an integer or decimal rounded to four decimal places as​ needed.)
 
​(c) Using the result in part​ (b), compute the probability that an adult from this country selected at random is male or bets on professional sports.
 
​P(male or bets on professional
​sports)=nothing
​(Type an integer or decimal rounded to four decimal places as​ needed.)
 
​(d) The poll data indicated that 7.1​% of adults in this country are males and bet on professional sports. What does this indicate about the assumption in part​ (b)?
 
A.
The assumption was correct and the events are independent.
 
B.
The assumption was incorrect and the events are not independent.
​(e) How will the information in part​ (d) affect the probability you computed in part​ (c)? Select the correct choice below and fill in any answer boxes within your choice.
 
A.
​P(males or bets on professional
​sports)=nothing
​(Type an integer or decimal rounded to four decimal places as​ needed.)
 
B.
This information does not affect the probability computed in part​ (c).
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