Respuesta :
Answer:
Total number of trials is 35.
Step-by-step 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 [tex]=\frac{3}{7}[/tex]
and probability of my friend's winning is [tex]=1-\frac{3}{7}=\frac{4}{7}[/tex]
Let there be n numbers of trials.
Therefore, my score after n trials [tex]=\frac{3n}{7}[/tex]
and my friend's score after n trials [tex]=\frac{4n}{7}[/tex]
Now, the number of trials my friend won more than me is
[tex]\frac{4n}{7}-\frac{3n}{7}=\frac{n}{7}[/tex]
We know, that my friend won 5 more trials than me so comparing the actual and given we get,
[tex]\frac{n}{7}=5\\n=7\times5=35[/tex]
Therefore, total number of trials is 35.
We can also verify our answer by placing value of n,
After 35 trials I will win [tex]\frac{3\times 35}{7}=15[/tex] trials
and my friend will win [tex]\frac{4\times 35}{7}=20[/tex] trials.
Hence, my friend won 5 more trials than me.
