1 . Let an experiment be rolling two dice and looking at the sum of the dice. Let event A = sum of the dice is less than 9 and let Event B = sum of the dice is odd

a) Are events A and B independent, dependent or mutually exclusive? Show why or why not

b) Give an example of an event C which can only involve a single die that is mutually exclusive of event A

2 . A woman is going to have fraternal twins (meaning not identical) and one is going to be a girl. What is the probability she will have two girls?

3 . Lithium batteries for a cell phone currently last 10 hours on average before they need to be recharged. Apple is developing a new Lithium battery, the problem is they are much more expensive, that they hope will last longer before it needs to be recharged. In a sample of 20 of these new batteries placed in cellphones the average time the batteries lasted before needing to be recharged was 10.8 hours with a standard deviation of 3 hours

a) At the .01 level do the new batteries last a statistically significant longer time? (p-value = .21)

b) Based on the results for a) would these batteries be something you would purchase ?Explain statistically