Statistics

Let P(U) = 0.19 and P(V) = 0.26. Events U and V are mutually exclusive. Find P(U or V). 5. A jar contains 10 red marbles numbered 1 to 10 and 4 blue marbles numbered 1 to 4. A marble is drawn at random from the jar. Find the probability that the marble is red AND odd-numbered. 6. Every cereal box has a gift inside, but you cannot tell from the outside what the gift is. The store manager assures you that 13 of the 45 boxes on the shelf have the secret decoder ring. The other 32 boxes on the shelf have a different gift inside. If you randomly select two boxes of cereal from the shelf to purchase, what is the probability that BOTH of them have the secret decoder ring? 7. Phi Delta Kappa (PDK) is an international professional organization for educators that, in collaboration with Gallup, has been conducting polls on the public's attitudes toward the public schools since 1969. The following was one of the questions on the most recent poll conducted June 4-13, 2011: "Most teachers in the nation now belong to unions or associations that bargain over salaries, working conditions, and the like. Has unionization, in your opinion, helped, hurt, or made no difference in the quality of public school education in the United States?" The respondents' answers broken down by party affiliation is shown below: Republican Democrat Independent Helped 35 146 69 Hurt 197 78 178 Made no difference 52 105 90 Don't know/refused 12 Round your probabilities to 4 decimal places, as needed. Calculate P(Republican) Calculate P(Republican | Helped) Using your answers above, are believing that unionization helped the quality of public school education in the United States independent or dependent of being Republican? Being Republican and believing that unionization helped the quality of public school education are ... O INDEPENDENT, since P(Republican) = P(Republican | Helped). O INDEPENDENT, since P(Republican) # P(Republican | Helped). O DEPENDENT, since P( Republican) = P(Republican | Helped)