Question
please answer all parts a through e
Question Help According to a poll about 17% of adults n a country bet on professional sports. Data indicates that 48 4% of the adult populaton in this country is male Complete parts (a) through (e) (a) Are the events "male and "bet on professional sports" mutually exclusive? Explain O A. Yes A person can be both male and bet on professional sports at the same time B. Yes A person cannot be both male and bet on professional sports at the same time. O C. No. A person cannot be male and bet on professional sports at the same time D., No A person can be both male and bet on professional sports at the same tme (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 bels 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 10 6% of adults n this country are males and beton professional sports what does this nicate about the assumption In part (b)? O A. The assumption was correct and the events are independent. O B. The assumption was incorrect and the events are not independent (e) How vwill he information in part (d) affect the probablty you computed in part (c? Select the correct chaice below and it in any answer boxes within your choice Click to select your answers).
Explanation / Answer
a. In logic and probability theory, two propositions (or events) are mutually exclusive or 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 above definition Answer is D. No, A person can be both male and bet of professional sports at the same time.
b. Here it is given that events are independent
So P(AnB)=P(A)*P(B)=0.17*0.484=0.08228
c. Now as we know P(AuB)=P(A)+P(B)-P(AnB)=0.17+0.484-0.08228=0.57172
d. Now it says P(AnB)=0.106 which is not equal to P(A)*P(B)
Hence answer is b. The assumption was incorrect and the events are not independent.
e. Based on d. P(AUB)=P(A)+P(B)-P(AnB)=0.17+0.484-0.106=0.548
