Question

use the table to answer each question round each answer to the nearest tenth of a percent, if necessary. favorite type of music hip hop country pop total grade level sophomore 21 10 4 35 junior 9 14 12 35 total 30 24 16 70 enter the answer in the space provided. use numbers instead of words. % use your answer to determine whether choosing hip hop music and being a sophomore are independent or dependent events. explain your reasoning enter the answer in the space provided

Explanation:

First Part (Calculating Percentage, e.g., Percentage of Sophomores who like Hip Hop or similar)

Let's assume we need to find the percentage of sophomores who like hip - hop.

Step 1: Identify the number of sophomores who like hip - hop and the total number of sophomores.

The number of sophomores who like hip - hop is 21, and the total number of sophomores is 35.

Step 2: Calculate the percentage.

The formula for percentage is $\text{Percentage}=\frac{\text{Number of sophomores who like hip - hop}}{\text{Total number of sophomores}}\times100\%$.
Substitute the values: $\frac{21}{35}\times100\% = 0.6\times100\%=60\%$.

Second Part (Determining if events are independent)

Two events $A$ (choosing hip - hop music) and $B$ (being a sophomore) are independent if $P(A\cap B)=P(A)\times P(B)$.

• Calculate $P(\text{Hip Hop})$: The total number of students who like hip - hop is 30, and the total number of students is 70. So $P(\text{Hip Hop})=\frac{30}{70}=\frac{3}{7}\approx0.4286$.
• Calculate $P(\text{Sophomore})$: The total number of sophomores is 35, and the total number of students is 70. So $P(\text{Sophomore})=\frac{35}{70}=0.5$.
• Calculate $P(\text{Hip Hop}\cap\text{Sophomore})$: The number of sophomores who like hip - hop is 21, and the total number of students is 70. So $P(\text{Hip Hop}\cap\text{Sophomore})=\frac{21}{70}=0.3$.

Now, calculate $P(A)\times P(B)$: $\frac{3}{7}\times0.5=\frac{3}{14}\approx0.2143$.

Since $P(\text{Hip Hop}\cap\text{Sophomore}) = 0.3$ and $P(\text{Hip Hop})\times P(\text{Sophomore})\approx0.2143$ and $0.3
eq0.2143$, the events are dependent.

First Answer (Percentage part)

60

Second Answer (Independence part)

The events of choosing hip - hop music and being a sophomore are dependent. Because $P(\text{Hip Hop}\cap\text{Sophomore})
eq P(\text{Hip Hop})\times P(\text{Sophomore})$ (0.3 is not equal to $\frac{3}{7}\times0.5\approx0.214$), so the two events are dependent.

Answer:

Step 1: Identify the number of sophomores who like hip - hop and the total number of sophomores.

The number of sophomores who like hip - hop is 21, and the total number of sophomores is 35.

Step 2: Calculate the percentage.

The formula for percentage is $\text{Percentage}=\frac{\text{Number of sophomores who like hip - hop}}{\text{Total number of sophomores}}\times100\%$.
Substitute the values: $\frac{21}{35}\times100\% = 0.6\times100\%=60\%$.

Second Part (Determining if events are independent)

Two events $A$ (choosing hip - hop music) and $B$ (being a sophomore) are independent if $P(A\cap B)=P(A)\times P(B)$.

• Calculate $P(\text{Hip Hop})$: The total number of students who like hip - hop is 30, and the total number of students is 70. So $P(\text{Hip Hop})=\frac{30}{70}=\frac{3}{7}\approx0.4286$.
• Calculate $P(\text{Sophomore})$: The total number of sophomores is 35, and the total number of students is 70. So $P(\text{Sophomore})=\frac{35}{70}=0.5$.
• Calculate $P(\text{Hip Hop}\cap\text{Sophomore})$: The number of sophomores who like hip - hop is 21, and the total number of students is 70. So $P(\text{Hip Hop}\cap\text{Sophomore})=\frac{21}{70}=0.3$.

Now, calculate $P(A)\times P(B)$: $\frac{3}{7}\times0.5=\frac{3}{14}\approx0.2143$.

Since $P(\text{Hip Hop}\cap\text{Sophomore}) = 0.3$ and $P(\text{Hip Hop})\times P(\text{Sophomore})\approx0.2143$ and $0.3
eq0.2143$, the events are dependent.

First Answer (Percentage part)

60

Second Answer (Independence part)

The events of choosing hip - hop music and being a sophomore are dependent. Because $P(\text{Hip Hop}\cap\text{Sophomore})
eq P(\text{Hip Hop})\times P(\text{Sophomore})$ (0.3 is not equal to $\frac{3}{7}\times0.5\approx0.214$), so the two events are dependent.