Your small business has two servers, Alan and Turing. There is an 8% chance that Alan crashes this week, and a 13% chance that Turing crashes this week. Hint: See Probability 2 notes, Example 1.4. 1. What is the probability there are no crashes this week? 2. What is the probability that exactly one crashes this week? 3. What is the probability that one or more crashes this week? ================================================================ You are dealt a 5 card hand from a standard 52 card deck. 1. What is the probability that you receive 2 fours and 3 kings? Hint: See solutions to Exercise 5.13.5. 2. What is the probability that you receive at least 3 kings? Hint: See solutions to Exercise 5.14.4. 3. What is the probability that you receive exactly 3 kings or exactly 3 hearts? Hint: See solutions to Exercise 5.14.3 and 5.14.4c. 4. You roll a die and pick a card. What is the probability that the number on the card is the same as the number on the die? Note: Treat an Ace as a 1. The Jack, Queen, King can be treated as 10's. Hint: See Participation Activities 5.13.3. 5. 6. A weighted die rolls a six on 20% of rolls. Other values from 1 to 5 each occur on 16% of rolls. Hint: See Participation Activity 5.13.2. 7. I roll the die. What is the probability I roll 4 or more? 8. I roll the die twice. What is the probability the first roll is 4 or more AND the second roll is a 6? 9. Repeat, but this time find the probability that one (or both) rolls are 4 or more. Hint: InclusionExclusion. Let S1 be the event the first roll is 4 or more. Let S2 be the event that the second roll is 4 or more