Question

according to a poll, about 14% of adults in a country bet on professional sports. data indicate that 46.4% 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. choose the correct answer
a. yes. a person cannot both be male and bet on professional sports at the same time
b. yes. a person can both be male and bet on professional sports at the same time
c. no. a person can both be male and bet on professional sports at the same time
d. no. a person cannot both be male and bet on professional sports at the same time.
(b) assuming that betting is independent of sex, 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.)

Explanation:

Step1: Recall the definition of mutually - exclusive events

Mutually - exclusive events are events that cannot occur at the same time. A person can be male and bet on professional sports simultaneously. So the events “male” and “bet on professional sports” are not mutually - exclusive.

Step2: Use the formula for the probability of the intersection of two independent events

If two events \(A\) and \(B\) are independent, \(P(A\cap B)=P(A)\times P(B)\). Let \(A\) be the event “male” and \(B\) be the event “bet on professional sports”. Given \(P(A) = 0.464\) and \(P(B)=0.14\).

$$P(\text{male and bets on professional sports})=P(\text{male})\times P(\text{bets on professional sports})$$

$$P = 0.464\times0.14$$

$$P=0.06496\approx0.0650$$

Answer:

(a) C. No. A person can both be male and bet on professional sports at the same time.
(b) \(0.0650\)