QUESTION 12 Conditional probability (reduced sample space) a) Among a group of 500 pet owners who visit the same pet store, it is found that 345 have a cat, while 375 have a dog. There are 290 of these who have both a dog and a cat. Suppose one individual is chosen at random from this group of 500 pet owners. Find the conditional probability the individual has a dog given that he or she has a cat. b.c) [use two way table from previous problem] Conditional Probability and Reduced Sample Space Consider the following two-way table representing the weather at a certain location 300 days Rain (>1 in) Sunny Cloudy No Rain 175 43 218 Little Rain (<1 in) 15 32 47 190 110 300 35 35 Find each of the probabilities b) Probability of no rain given that it is a sunny day, Pr(No Rain | Sunny) C) Probability of a sunny day given that there is no rain, Pr (Sunny | No Rain)

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