Question

685 gym members were asked if they use the elliptical machine or treadmill as their primary cardiovascular exercise. 257 said they use the treadmill, 157 said they use the elliptical, and 85 said they use both.
a.) Organize this using a venn diagram (2 marks)

b.) A gym member is chosen from this group. What is the probability that this member uses the treadmill only? (1 mark)

Answer 1

Given:

Total number of gym members = 685

257 said they use the treadmill, 157 said they use the elliptical, and 85 said they use both.

To find:

a. The venn diagram.

b. The probability that a member uses the treadmill only?

Solution:

(a)

We have,

Total number of gym members = 685

Treadmill user = 257

Elliptical user = 157

Who use both = 85

Only treadmill user is:

$257-85=172$

Only Elliptical used

$157-85=72$

Therefore, the venn diagram for the given situation is shown below.

(b)

The member who use treadmill only = 172

Total user = 685

The probability that a member uses the treadmill only is:

$P(\text{Only treadmill})=\dfrac{\text{Only treadmill users}}{\text{Total users}}$

$P(\text{Only treadmill})=\dfrac{172}{685}$

Therefore, the probability that a member uses the treadmill only is $\dfrac{172}{685}$.