The annual Atlantic Coast Conference men’s basketball tournament has temporarily taken Joe’s mind off of the Cleveland Indians. He says to himself, "I think that Notre Dame has probability 0.05 of winning. North Carolina’s probability is twice Notre Dame’s, and Duke’s probability is four times Notre Dame’s." (a) What is Joe's personal probability for North Carolina? (Enter your answer as a proportion rounded to one decimal place.) P (North Carolina wins) = What is Joe's personal probability for Duke? (Enter your answer as a proportion rounded to one decimal place.) P (Duke wins) = (b) What is Joe's personal probability that 1 of the 12 teams other than Notre Dame, North Carolina, and Duke will win the tournament? (Enter your answer as a proportion rounded to two decimal places.) P=

a. Joe's personal probability for North Carolina is 0.1

Joe's personal probability for Duke is 0.2

b. Joe's personal probability that 1 of the 12 teams other than Notre Dame, North Carolina, and Duke will win the tournament is 0.65

Step-by-step explanation:

a. According to the given data, to calculate Joe's personal probability for North Carolina we would have to make the following calculation:

Joe's Personal P(North Carolina Wins)=Joe's Personal P(Notre Dame wins) × 2

Joe's Personal P(North Carolina Wins)= 0.05×2

Joe's Personal P(North Carolina Wins)=0.1

Joe's personal probability for North Carolina is 0.1

To calculate Joe's personal probability for Duke we would have to make the following calculation:

P(Duke wins)=Joe's Personal P(Notre Dame wins) × 4= 0.05×4 = 0.2

Joe's personal probability for Duke is 0.2

b. To calculate Joe's personal probability that 1 of the 12 teams other than Notre Dame, North Carolina, and Duke will win the tournament we would have to make the following calculation:

P( 1 of the 12 teams other than Notre Dame, North Carolina and Duke wins)= 1- P( Notre dame or north north ca or duke wins)=1-(0.05+0.1+0.2)=1-0.35=0.65

Joe's personal probability that 1 of the 12 teams other than Notre Dame, North Carolina, and Duke will win the tournament is 0.65

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step-by-step explanation: