4. People don’t always answer surveys honestly! Suppose that the number of students at a school who really like the taste of canned peas is 6%. And suppose that when students who DO like them are surveyed, 90% of them say honestly that they do like them, whereas the others say falsely that they don’t like them. When the survey is given to students who really DO NOT like canned peas, 95% of those asked will honestly say they don’t, but the remaining ones falsely say they do like them. If a student SAYS he/she DOES like the taste of canned peas, what is the probability that they really do? (You may express your answer as either a fraction or a percentage.)

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4. People don’t always answer surveys honestly! Suppose that the number of students at a school who really like the taste of canned peas is 6%. And suppose that when students who DO like them are surveyed, 90% of them say honestly that they do like them, whereas the others say falsely that they don’t like them. When the survey is given to students who really DO NOT like canned peas, 95% of those asked will honestly say they don’t, but the remaining ones falsely say they do like them. If a student SAYS he/she DOES like the taste of canned peas, what is the probability that they really do? (You may express your answer as either a fraction or a percentage.)

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The event A is defined as the students at a school who really like the taste of canned peas, and  A¯ is students at a school who really do not like the taste of canned peas, D is defined as the students do like them are surveyed.

From the given information PA=0.06,PA¯=0.94PD|A=0.90,PD|A¯=0.05.

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