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

Total number of trials is 35.

Explanation:

Given : 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.

To find : How many trials are in the competition?

Solution :

Probability of my winning is 3 out of 7 trials
`=(3)/(7)`

and probability of my friend's winning is
`=1-(3)/(7)=(4)/(7)`

Let there be n numbers of trials.

Therefore, my score after n trials
`=(3n)/(7)`

and my friend's score after n trials
`=(4n)/(7)`

Now, the number of trials my friend won more than me is

`(4n)/(7)-(3n)/(7)=(n)/(7)`

We know, that my friend won 5 more trials than me so comparing the actual and given we get,

`(n)/(7)=5\\n=7*5=35`

Therefore, total number of trials is 35.

We can also verify our answer by placing value of n,

After 35 trials I will win
`(3* 35)/(7)=15` trials

and my friend will win
`(4* 35)/(7)=20` trials.

Hence, my friend won 5 more trials than me.