SOLUTION: A student conducted a survey at school and found that 75 % of the boys and 65 % of the girls like to watch hockey games. There are an equal number of boys and girls in the school.

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Question 1182188: A student conducted a survey at school and found that 75 % of the boys and 65 % of the girls like to watch hockey games. There are an equal number of boys and girls in the school. If someone does not like to watch hockey games, what is the approximate probability that the person is a boy?
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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A student conducted a survey at school and found that 75 % of the boys and 65 % of the girls
like to watch hockey games. There are an equal number of boys and girls in the school.
If someone does not like to watch hockey games, what is the approximate probability that the person is a boy?
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Let x be the number of boys in the school.

Then the number of girls also ix x, according to the condition.



The number of boys who does not like to watch hockey games is  0.25x.


The number of those who does not like to watch hockey games is  0.25x + 0.35x = 0.6x.



The probability under the question is 


    P = %280.25x%29%2F%280.25x+%2B+0.35x%29 = %280.25x%29%2F%280.6x%29 = 0.25%2F0.6 = 25%2F60 = 5%2F12.    ANSWER

Solved.



Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Let's say there are 2000 people at this school. You can pick any number you want as long it's a positive whole number. I'm picking this value because taking various percentages of it will result in whole numbers as well.

Because there are an equal number of boys and girls, this means there are 1000 of each gender.

75% of the boys like hockey, telling us that 0.75*1000 = 750 boys like hockey. So 1000-750 = 250 boys do not like hockey. You could also say 0.25*1000 = 250 to represent 25% of 1000.

65% of the girls like hockey, so 35% of the girls do not like hockey. We can then say 0.35*1000 = 350 girls do not like hockey.

In total, we have 250+350 = 600 people who do not like hockey. Of this total, 250 boys do not like hockey.

Therefore, we end up with this probability:
250/600 = (5*50)/(12*50) = 5/12

This is effectively saying: if we had a group of 12 people who don't like hockey, then there are 5 boys in this group (and picking a boy randomly from this group has probability 5/12)

You should find that 5/12 = 0.4167 approximately when using a calculator.

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Answer in fraction form = 5/12
Answer in decimal form = 0.4167 (approximate)
Answer in percent form = 41.67% (approximate)