At a school, 43% of students attend the homecoming football game, 48% of students attend the homecoming dance, and 23% of students attend the game and the dance.a. What is the probability that a student who attends the football game also attends the dance? Express your first answer as a simplified fraction and your percent answer rounded to the tenths place. , or about $\%$%b. What is the probability that a student who attends the dance also attends the football game? Express your first answer as a simplified fraction and your percent answer rounded to the tenths place. , or about $\%$
Question
At a school, 43% of students attend the homecoming football game, 48% of students attend the homecoming dance, and 23% of students attend the game and the dance.a. What is the probability that a student who attends the football game also attends the dance? Express your first answer as a simplified fraction and your percent answer rounded to the tenths place. , or about %b. What is the probability that a student who attends the dance also attends the football game? Express your first answer as a simplified fraction and your percent answer rounded to the tenths place. , or about
Solution
a. The probability that a student who attends the football game also attends the dance is calculated by dividing the percentage of students who attend both events by the percentage of students who attend the football game.
So, we have 23% (students who attend both) divided by 43% (students who attend the football game).
In fraction form, this is 23/43. This fraction cannot be simplified any further.
To convert this to a percentage, we divide 23 by 43 and multiply by 100, which gives us approximately 53.5%. Rounded to the tenths place, this is 53.5%.
b. The probability that a student who attends the dance also attends the football game is calculated by dividing the percentage of students who attend both events by the percentage of students who attend the dance.
So, we have 23% (students who attend both) divided by 48% (students who attend the dance).
In fraction form, this is 23/48. This fraction cannot be simplified any further.
To convert this to a percentage, we divide 23 by 48 and multiply by 100, which gives us approximately 47.9%. Rounded to the tenths place, this is 47.9%.
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