# How would I go about solving this probability question?

I am currently in year 10 studying GCSE higher maths. My once issue with maths is probability. I have an exam tomorrow and am currently revising by going through past papers, I saw this question and wasn't sure how I'd solve it. Does anyone have an idea?

A school has 400 boys and 500 girls.
The probability that a boy is vegetarian is 0.1
The probability that a girl is vegetarian is 0.2
Estimate the total number of vegetarians in the school.

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Count the number of vegetarian boys. Count the number of vegetarian girls. Add. – Did Feb 27 '14 at 20:12
Yes but how would I count how many there are? – Harry Kitchener Feb 27 '14 at 20:14
How many boys must be vegetarian to get that probability? – Ross Millikan Feb 27 '14 at 20:15
Are you asking me @Ross? If so, I don't know this is a past paper set by AQA. – Harry Kitchener Feb 27 '14 at 20:16
The probability that a boy is a vegetarian is $P[x\in V\vert\, x\in B]$. The probability that a student is a boy and a vegetarian is $P[x\in B \textrm{ and } x\in V]$. These quantities are connected by the conditional probability formula: $$P[x\in V \vert \, x\in B]=\frac{P[x\in V \textrm{ and } x\in B]}{P[x\in B]}.$$ Clearly, $P[x\in B]=\frac{4}{9}$. – Unwisdom Feb 27 '14 at 21:02

Estimated number of boy vegetarians is $400 \cdot 0.1=40$.
Estimated number of girl vegetarians is $500 \cdot 0.2=100$.
Both sums up to $140$.