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1. John is going to a New Year's celebration. He will bring two dishes to share with his friends but has not yet decided what to bring. He will bring one main dish and one dessert. For the main dish he will choose to bring dumplings or spring rolls. For the dessert he will choose rice cakes or egg tarts. Here is some additional information.
• John will bring dumplings with probability 0.6.
• If John brings dumplings, then the probability that he brings rice cakes is 0.72.
• If John brings spring rolls, then the probability that he brings egg tarts is 0.25.
1.1. What is the probability John brings rice cakes to the New Year's celebration?
1.2. Assuming John brings egg tarts to the party, what is the probability he brings spring rolls?
1.3. Is John's choice of main dish independent of his choice of dessert? Justify your answer mathematically.
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