Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
We have been given that 1/2 of the children at a party like chocolate ice cream, 2/3 like vanilla ice cream, and 1/3 like chocolate and vanilla.
To find the fraction of children, who like vanilla also like chocolate, We will divide the fraction of children who like chocolate and vanilla by the fraction of children who like vanilla.
[tex]\text{Fraction of those who like vanilla also like chocolate}=\frac{\frac{1}{3}}{\frac{2}{3}}[/tex]
Since we know that dividing a fraction by another fraction is same as multiplying the first fraction by the reciprocal of second fraction.
[tex]\text{Fraction of those who like vanilla also like chocolate}=\frac{1}{3}\times\frac{3}{2}[/tex]
After cancelling out 3 from numerator and denominator of our fraction, we will get,
[tex]\text{Fraction of those who like vanilla also like chocolate}=\frac{1}{2}[/tex]
Therefore, the fraction of those who like vanilla also like chocolate is [tex]\frac{1}{2}[/tex].
