QuestionFind the probability that a student not playing board games also doesn't play video games. Round to two decimal places.

Studdy Solution

STEP 1

Assumptions1. The total number of students who play video games is15. . The total number of students who play both video games and board games is9.
3. The total number of students who play board games is19.
4. The total number of students who do not play either video games or board games is7.

STEP 2

First, we need to find the total number of students. This can be done by adding the number of students who play video games, the number of students who play board games, and the number of students who do not play either, but remember to subtract the number of students who play both games because they were counted twice.
$Total\, students = Video\, games + Board\, games + Neither - Both$

STEP 3

Now, plug in the given values for the number of students who play video games, board games, both, and neither to calculate the total number of students.
$Total\, students =15 +19 +7 -9$

STEP 4

Calculate the total number of students.
$Total\, students =15 +19 +7 -9 =32$

STEP 5

Next, we need to find the number of students who do not play board games. This can be done by subtracting the number of students who play board games from the total number of students.
$No\, board\, games = Total\, students - Board\, games$

STEP 6

Plug in the values for the total number of students and the number of students who play board games to calculate the number of students who do not play board games.
$No\, board\, games =32 -19$

STEP 7

Calculate the number of students who do not play board games.
$No\, board\, games =32 -19 =13$

STEP 8

Now, we can find the probability that a randomly selected student who does not play board games also does not play video games. This can be done by dividing the number of students who do not play either game by the number of students who do not play board games.
$Probability = Neither / No\, board\, games$

STEP 9

Plug in the values for the number of students who do not play either game and the number of students who do not play board games to calculate the probability.
$Probability =7 /13$

STEP 10

Calculate the probability.
$Probability =7 /13 \approx0.5385$

STEP 11

To express the probability as a percentage, we multiply the decimal value by100.
$Probability\, (\%) = Probability \times100$

STEP 12

Plug in the decimal value of the probability to calculate the percentage.
$Probability\, (\%) =0.5385 \times100$

STEP 13

Calculate the probability percentage.
$Probability\, (\%) =0.5385 \times100 \approx53.85\%$ The probability that a randomly selected student who does not play board games also does not play video games is approximately53.85%.

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