Math solve

5. Determine the probability of rolling each of the following totals with a standard pair of dice. Illustrate each with a Venn diagram. a. a 2 or an 8 b. a number less than 4 or an even number c. 7, 11, or doubles d. a prime number or a perfect square 6. 74% of the population subscribes to a newspaper. 46% of the population subscribes to a magazine. Assuming that these are independent events. a. Are these events mutually exclusive? Why or why not? b. Find the probability that a household only subscribes to the newspaper. c. Find the probability that a household doesn't subscribe to either. d. Find the probability that a household subscribes to either the newspaper or magazines. 7. Lauren is the point guard on her basketball team. She estimates that her chances of getting a 3-pointer are 85% when there is no one defending against her, but only 60% when there is a defender. There is a 50% chance that the girl assigned to defend her will not be close enough to block the shot. What is the probability of Lauren scoring a 3-point shot? 8. Which is more likely: event A, drawing an ace, then a king, then a queen, or event B, drawing three consecutive aces? Assume that cards drawn are not returned to the pack. How does your answer change if cards are returned after each draw? Explain how you determined your answers. 9. Ben, Anna, and Mark are going out for pizza. They can get a pizza with 3 toppings and decide to each pick one topping. The choices of toppings are pepperoni, hamburger, sausage, onions, bell peppers, olives, and anchovies. If they choose at random, what is the probability that they both choose the same topping? 10. The Canadian Cancer Society has estimated that 1 in every 3 Canadians will have cancer in their lifetime. Suppose that a resear lab has developed a test that is 98% accurate for people that have Cancer and 95% accurate for those that do not. If the lab chooses a person at random to take the test, what is the probability that the diagnosis is correct