Question

a group of campers were polled about whether they like swimming and whether they like playing baseball. the data from the survey is shown in the venn diagram. use the venn diagram to find the missing values in the frequency table. swimming vs. baseball swimming vs. baseball which values are correct? select three options. $a = 15$ $b = 18$ $c = 23$ $d = 35$ $e = 31$

Explanation:

Step1: Find value of a

$a = 15$

Step2: Find value of b

$b = 18 + 13 = 31$

Step3: Find value of c

$c = 24 + 15 = 39$

Step4: Find value of d

$d = 24 + 15 + 18 + 13 = 70$

Step5: Find value of e

$e = 18 + 13 = 31$

Answer:

A. $a = 15$
E. $e = 31$
*Note: Upon rechecking, the correct three valid options are $a=15$, $e=31$, and correcting the earlier miscalculation for $b$: $b$ is "Does Not Like Swimming" total, which is $18+13=31$, so the three correct options are:
A. $a = 15$, E. $e = 31$, and there is a correction: the value for "Does Not Like Swimming, Likes Baseball" is 18, but $b$ is the total for Does Not Like Swimming, so the correct valid options are:
A. $a = 15$,
B. $b = 31$ (corrected from original option label, but matching the provided option E: $e=31$ and A: $a=15$, and the third correct value is that $c=24+15=39$ is not listed, so the three correct options from the given choices are:
A. $a = 15$,
E. $e = 31$,
and correcting the error: the value for "Does Not Like Swimming, Likes Baseball" is 18, but $b$ is the total of Does Not Like Swimming, so the given option $b=18$ is incorrect, $d=35$ is incorrect, $c=23$ is incorrect. The only correct options are A. $a = 15$ and E. $e = 31$? No, re-reading the table:
The table rows are:

• Likes Baseball, Does Not Like Baseball, Total

Columns: Likes Swimming, Does Not Like Swimming, Total

So:
$a$ = Likes Swimming and Likes Baseball = 15
$b$ = Does Not Like Swimming and Likes Baseball = 18
$c$ = Total Likes Baseball = 15+18=33 (not 23, so option c is wrong)
$d$ = Total Likes Swimming = 24+15=39 (not 35, wrong)
$e$ = Total Does Not Like Swimming = 18+13=31

So the three correct options are:
A. $a = 15$,
B. $b = 18$,
E. $e = 31$

Correcting the earlier table misinterpretation:

Step1: Define $a$ (Swim+Baseball)

$a = 15$

Step2: Define $b$ (No Swim+Baseball)

$b = 18$

Step3: Define $e$ (Total No Swim)

$e = 18 + 13 = 31$

Final Answer:

A. $a = 15$
B. $b = 18$
E. $e = 31$