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Prepare a Venn diagram giving the probabilities for each distinct area; then answer the questions posed. A survey of 168 boys aged 6 to 12 revealed the following information: 74 of them liked chocolate cake, 89 of them liked golden cake and 23 liked both.

A) What is the probability that a boy liked golden cake, given that he liked chocolate cake?

B) What is the probability that a boy didn't like golden cake given that he liked chocolate cake?

C) Are liking chocolate cake and not liking golden cake statistically independent? Give mathematical proof.

Any help regarding this question would be greatly appreciated as I find it quite confusing how to calculate the areas of the Venn Diagram and the following questions. I understand I am using formulas such as P(A|B) for the questions, but I am still very, very confused by the question.

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