Question

2 fill in the blank 50 points use the venn diagram to answer the questions. round to the hundredths place (2 decimal places). rock rap 18 11 24 7 8 1 17 country a) how many total people are represented in the diagram? type your answer... b) how many people like country music? type your answer... c) if one person is chosen at random, what is the probability that the person will like rap music? type your answer... d) if one person is chosen at random, what is the probability that the person will like country or rock music? type your answer... e) if one person is chosen at random, what is the probability that the person will like country and rock music? type your answer...

Explanation:

Part A: Total People

Step1: Sum all regions

Add all numbers in Venn diagram: \( 18 + 11 + 24 + 8 + 7 + 1 + 17 \)

Step2: Calculate total

\( 18+11=29 \), \( 29+24=53 \), \( 53+8=61 \), \( 61+7=68 \), \( 68+1=69 \), \( 69+17=86 \)

Step1: Identify Country regions

Regions in Country circle: \( 8 \) (Rock-Country), \( 7 \) (all three), \( 1 \) (Rap-Country), \( 17 \) (only Country)

Step2: Sum these regions

\( 8 + 7 + 1 + 17 = 33 \)

Step1: Find Rap total

Regions in Rap circle: \( 11 \) (Rock-Rap), \( 24 \) (only Rap), \( 7 \) (all three), \( 1 \) (Rap-Country) → \( 11 + 24 + 7 + 1 = 43 \)

Step2: Probability = Rap total / Total people

\( \frac{43}{86} = 0.50 \) (simplifies as \( 43 \div 86 = 0.5 \), rounded to hundredths is \( 0.50 \))

Answer:

86

Part B: People who like Country