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)
p(male and bets on professional sports) = 0.0650
(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) = 0.5390
(type an integer or decimal rounded to four decimal places as needed.)
(d) the poll data indicated that 8.4% of adults in this country are males and bet on professional sports. what does this indicate about the assumption in part (b)? choose the correct answer.
○ 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 and, if necessary, fill in the answer box within your choice.
○ a. p(male 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:

Step1: Recall the formula for \(P(A\cup B)\)

The formula for the probability of the union of two events \(A\) and \(B\) is \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\). Let \(A\) be the event that an adult is male and \(B\) be the event that an adult bets on professional sports. We know \(P(A) = 0.464\), \(P(B)=0.14\). In part (d), \(P(A\cap B) = 0.084\)

Step2: Substitute the values into the formula

Substitute \(P(A) = 0.464\), \(P(B)=0.14\), and \(P(A\cap B)=0.084\) into the formula \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\). So \(P(A\cup B)=0.464 + 0.14-0.084\)

Step3: Calculate the result

\(0.464+0.14 - 0.084=(0.464 + 0.14)-0.084=0.604-0.084 = 0.52\)

Answer:

A. \(P(\text{male or bets on professional sports})=0.5200\)