4.Suppose there is a card game where you are dealt a hand of three cards. You have already learned that the total number of three-card hands that can be dealt from a deck of 52 cards is:

In this problem you will calculate the probability of getting a hand that has exactly two aces in it(A A X). You will do this by finding out the number of possible hands that have exactly two aces, and then dividing by the total possible number of three-card hands that is stated above.

Part A:Use themultiplication principleto tell the total number of three-card hands (permutations) that can be made with two aces.(2 points)

Part B:In the answer from Part I, each two-ace hand got counted twice. For example, AAX got counted as a separate hand from AAX. Since order should not matter in a card hand, these are really the same hand. What is the actual number of two-ace hands (combinations) you can get from a deck of 52 cards?(2 points)

Part C:Find the probability of drawing a three-card hand that includes two aces from a deck of 52 cards. Write your answer as a fraction.(2 points)

5.A 2011 study by The National Safety Council estimated that there are nearly 5.7 million traffic accidents year. At least 28% of them involved distracted drivers using cell phones or texting. The data showed that 11% of drivers at any time are using cell phones . Car insurance companies base their policy rates on accident data that shows drivers have collisions approximately once every 19 years. That's a 5.26% chance per year. Given what you know about probability, determine if cell phone use while driving and traffic accidents are related.

Step A:LetDC= event that a randomly selected driver is using a cell phone. What isP(DC)?(1 point)

Step B:LetTA= event that a randomly selected driver has a traffic accident. What isP(TA)? Hint: What is the probability on any given day?(1 point)

Step C:How can you determine if cell phone use while driving and traffic accidents are related?(1 point)

Step D:Given that the driver has an accident, what is the probability that the driver was distracted by a cell phone? Write this event with the correct conditional notation.(1 point)

Step E:What is the probability that a randomly selected driver will be distracted by using a cell phone and have an accident?(2 points)

Step F:For a randomly selected driver, are the events "driving while using a cell phone" and "having a traffic accident" independent events? Explain your answer.(2 points)