Question

1. on a recent survey, students were asked if they ice skate, snowboard, or ski. the venn diagram below shows the results of the survey.

a. how many students ski or snowboard?
b. how many students ice skate and ski?
c. how many students ice skate, ski, and snowboard?
d. how many students do not ski or ice skate?
e. how many students just snowboard?
f. how many students do not ice skate, ski, or snowboard?
g. how many students ice skate?
h. how many students do not snowboard?
i. how many students took the survey?

Explanation:

Step1: Find total number of students who took the survey

Sum all the numbers in the Venn - diagram.
$6 + 7+4 + 3+2+8 + 13+10=53$

Step2: Find number of students who ice - skate and ski

Look at the intersection of ice - skate and ski circles.
$2 + 3=5$

Step3: Find number of students who ice - skate, ski, and snowboard

Look at the triple - intersection.
$3$

Step4: Find number of students who do not ski or ice - skate

Sum the parts of the snowboard circle that do not intersect with ice - skate or ski circles.
$10$

Step5: Find number of students who just snowboard

The part of the snowboard circle that does not intersect with other circles.
$10$

Step6: Find number of students who do not ice - skate, ski, or snowboard

The number outside the three circles.
$6$

Step7: Find number of students who do not snowboard

Sum all parts not in the snowboard circle.
$6+7 + 2+13=28$

Step8: Find total number of students who took the survey (repeated for clarity)

Sum all values in the diagram.
$6+7 + 4+3+2+8+13+10 = 53$

Answer:

a. $53$
b. $5$
c. $3$
d. $10$
e. $10$
f. $6$
g. $28$
h. $53$