Question

A recent survey of active adults found that 65% of them regularly bike ride for exercise, 45% are runners and 30% ride and run.
a) Using a Venn diagram or otherwise, find the percentage of these adults that:

i) ride or run (1 mark)

A. 30%
B. 110%
C. 50%
D. 20%
E. 80%
Enter the letter only

ii) only run (1 mark)

A. 45%
B. 30%
C. 35%
D. 15%
E. 20%
Enter the letter only.

iii) if they are runners also ride

A. 66.7%
B. 30%
C. 20%
D. 46.2%
E. 15%
Enter the letter only.

iv) neither run nor ride (1 mark)

A. 70%
B. 15%
C. 35%
D. 20%
E. 80%
Enter the letter only.

b) Are running and riding mutually exclusive? (1 mark)

A. Yes, because adults only ride or run
B. Yes, because riding a bike doesn’t affect the likelihood of being a runner.
C. No, because an adult can bike ride and run for exercise.
D. No, because riding a bike and running are independent events.
E. Yes, because an adult can ride and run for exercise.

c) In a randomly selected group of 7 active adults, calculate the probability that exactly 3 of them bike ride and run for exercise.

A. 0.006
B. 0.015
C. 0.097
D. 0.227
E. 0.314

Answer 1

ANSWER :-) answer to your question is

a)  i) Ride or run : answer to this is as follows

E) 80%   {   65+ (45-30) = 80%}

ii) Only run : answer to this is as follows

D) 15% { 45-30=15%}

iii) If they are runners also ride :answer to this is as follows

B) 30%

iv) Neither run or ride : answer to this is as follows

D) 20% ( 1-80%=20%)

b)  C). No, because an adult can bike ride and run for exercise.

c) A) 0.006

The probability that exact three of them bike ride is = 1/7*1/6*1/5

=0.006