According to a poll, about 14% of adults in a country bet on professional sports

Question

According to a poll, about 14% of adults in a country bet on professional sports. Data indicates that 47.9% 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. No. A person can be both male and bet on professional sports at the same time. B. Yes. A person can be both male and bet on professional sports at the same time. C. Yes. A person cannot be both male and bet on professional sports at the same time. D. No. A person cannot be 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) = (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) = (Type an integer or decimal rounded to four decimal places as needed.) (d) The poll data indicated that 8.7% 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 incorrect and the events are not independent. B. The assumption was correct and the events are 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) = (Type an integer or decimal rounded to four decimal places as needed.) B. This information does not affect the probability computed in part (c).

Explanation / Answer

a In logic and probability theory, two propositions (or events) are mutually exclusiveor disjoint if they cannot both be true (occur). A clear example is the set of outcomes of a single coin toss, which can result in either heads or tails, but not both.

Based on this answer is A. A person can be both male and bet on professional sports at the same time.

b. As it is asked to assumed both events are independent. So P(A and B)=P(A)*P(B)=0.14*0.479=0.06706

c. Here we need to find P(AuB)=P(A)+P(B)-P(AnB)=0.14+0.479-0.06706=0.55194

d. Events areindependent if the occurrence of one event does not influence (and is not influenced by) the occurrence of the other(s).

So assumption was wrong as P(AnB)=0.06706 and here it comes to be P(AnB)=0.087

Hence answer is assumption was incorrect and the events are not independent.

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