1. Out of the 2000 students who attend a certain high school, 1400 students own cell phones, 1000 own a tablet, and 800 have both. Suppose a student is randomly selected. Create a Venn diagram model below.
Previously, we've learned conditional probability:[br][math]P\left(A|B\right)=\frac{P\left(A\cap B\right)}{P\left(B\right)}[/math][br]and talked about the conditions for independence:[br]A and B are independent if [math]P\left(A|B\right)=P\left(A\right)andP\left(B|A\right)=P\left(B\right)[/math][br]If A and B are independent, then [math]P\left(A\cap B\right)=P\left(A\right)·P\left(B\right)[/math][br][br]Use this knowledge and mathematical notation to answer the following:[br]a. What is the probability that a randomly selected student owns a cell phone?[br]b. What is the probability that a randomly selected students owns both a cell phone and a tablet?[br]c. If a randomly selected student owns a cell phone (was one of the 1400 with a phone), what is the probability that this student also owns a tablet?[br]d. How are questions b and c different?[br]e. Are the outcomes owns a cell phone and owns a tablet independent? Explain.[br]f. If question e is not independent, change the conditions of the problem to make them independent