Statistics and Probability

The correct size of a nickel is 21.21 millimeters. Based on that, the data can be summarized into the following table indicating the numbers of children from each income group who drew the nickel too small and too large: Too Small Too Large Total Low Income 8 12 20 High Income 12 3 15 Total 20 15 35 a) The proportion of children from the low income group that drew the nickel too large is: b) The proportion of children from the high income group that drew the nickel too large is: c) The proportion of all children that drew the nickel too large is: d) If a child is picked at random, what is the probability they are in the low income group, given they drew the nickel too large? e) If a child is picked at random, what is the probability they are in the high income group OR drew the nickel too large? 2 Giving a test to a group of students, the grades and shirt colors are summarized below A B C Total Red Shirt 8 3 19 30 Blue Shirt 18 10 16 44 Total 26 13 35 74 If one student is chosen at random, (a) Find the probability that the student has a Red Shirt GIVEN they got a 'A'. Round to 4 decimal places, if needed. (b) Find the probability that the student got a 'A' GIVEN they are wearing a Red Shirt. 3 65% of all Californians registered voters prefer life in prison without parole over the death penalty for a person convicted of first-degree murder. Among Latino California registered voters, 34.5% prefer life in prison without parole over the death penalty for a person convicted of first-degree murder. 41.8% of all Californians are Latino. These preferences are summarized in the contingency table below: Latino Non-Latino Total Prefer Life Sentence 0.18975 0.36025 0.55 Prefer Death Penalty 0.22825 0.22175 0.45 Total 0.418 0.582 Suppose that one Californian is randomly selected. Round your answers to parts a) and b) to two decimal places. a) What is P(C) ? b) What is P(C | L) ? c) Are C and L independent events