Let A and B be independent events, such that P(A) = 0.9639 and P(B) = 0.6521. Find the following probabilities: P(A and B)= % (Round the answer to 2 decimals) Assume that the probability that a randomly selected student is in middle school is 0.6122 and the probability that a randomly selected student is in public school is 0.6121. Assuming that the two events are independent, find the probability that a randomly selected students is in public middle school: P(A and B)= (Round the answer to 4 decimals) Assume that the probability that a randomly selected student is normal is 0.5399 and the probability that a randomly selected student is a female is 0.8011. Assuming that the two events are independent, find the probability that a randomly selected student is female that is normal: P(A and B)= % (Round the answer to 2 decimals) The following contingency table summarizes the drug test results for 410 test-takers: Doesn't use drugs Uses drugs Total Positive 3 231 Negative 164 12 Total For a randomly selected test administration, find the following probabilities. (Round the answers to 4 decimal places.) 1) The probability that the test-taker doesn't use drugs: 2) The probability of a true negative: 3) The probability of an error: 4) The positive predicting value: