Question

you and a friend have a hula hoop competition. you win 3 out of every 7 trials. your friend wins 5 more trials than you. how many trials are in the competition?

Answer 1

We have been given that me and my friend have a hula hoop competition. I win 3 out of every 7 trials. My friend wins 5 more trials than me.  

Probability of my winning is $\frac{3}{7}$ and probability of my friend's winning is $\frac{4}{7}$.    

Let there be n numbers of trials. Therefore, my score after n trials is $\frac{3n}{7}$ and my friend's score after n trials is $\frac{4n}{7}$.

Therefore, trials my friend won more than be would be,

$\frac{4n}{7} -\frac{3n}{7} =\frac{n}{7}$

We have been given that my friend won 5 more trials than me. So upon equating these two quantities we will get,

$\frac{n}{7}=5$

$n=7\times 5=35$

Therefore, total number of trials is 35.

Let us verify our answer.

After 35 trials I will win $35\times\frac{3}{7} =5\times3=15$trials and my friend will win $35\times\frac{4}{7} =5\times4=20$ trials. Hence, my friend won 5 more trials than me.