Education subject preferences. An article published in the Chinese Journal of Sociology (Vol. 6, 2020) presents comparative evidence on the gender gap in educational achievement in Japan, China, and the United States. It highlights the gender-specific impact of parental income and education on a child’s own preference of study subjects. The boys and girls from Japan who were part of the survey were asked to share which subjects they liked. Their numbers of boys and girls who preferred linguistics and math are listed in the following table. One of the 823 children is randomly selected. Boys Girls Totals Likes Math 254 192 446 Likes Linguistics 159 218 377 Totals 413 410 823 Source: Hideo Akabayashi et al., “Gender Differences in Educational Outcomes and the Effect of Family Background: A Comparative Perspective from East Asia,” Chinese Journal of Sociology, Vol. 6, No. 2, 2020.

a. Find the probability that the randomly selected child likes math.

b. Given the child selected is a boy, find the probability that he likes math.

c. Given the child selected is a girl, find the probability that she likes math.