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Exercise Set 7.4: Probability of Independent Events Find the number of possibilities for the given situations. 1. The nu...

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Exercise Set 7.4: Probability of Independent Events Find the number of possibilities for the given situations. 1. The number of unique words you can make using the letters {A, B, C, D}. 2. What is the number of unique 4-digit ATM PIN codes if the first number cannot be 0? 3. What is the number of possible unique screen names if DAN wants to use the arrangement of his first name followed by arrangements of the year of his birth 1987? 4. What is the number of unique possible screen names if ADAM wants to use the arrangement of his first name followed by arrangements of the year of his birth 1995? 5. What is the possible number of unique license plates if the first digit must be a number, the next three digits must be a letter, and the last three digits must be numbers? Find the probability that each of the following events will occur. 6. What is the probability that you roll either a 5 or a 6 on a die? 7. What is the probability that you roll a 2, 3, or 4 on a die? 8. What is the probability that you roll a total of 6 on two dice? 9. What is the probability that you roll a total of 7 on two dice? 10. What is the probability that you roll a total of less than 8 on two dice? 11. You flip a coin where one side is heads and the other side is tails. What is the chance that you will flip heads three times in a row? 12. You flip a coin four times where one side is heads and the other side is tails. What is the chance that you will flip heads the first two times and tails the second two times.

13. At the time of your turn, a particular Scrabble bag contains 8 Es, 3 Ds, 5 As, and 2 Ts. What is the probability that you will pull a D? 14. At the time of your turn, a particular Scrabble bag contains 5 Es, 3 Rs, 4 Os, and 5 As. What is the probability that you will pull an R? 15. A bag of marbles contains 7 large red marbles, 5 large yellow marbles, 3 small red marbles, and 5 small yellow marbles. If you draw a marble at random, what is the probability that you will draw a red marble, given that it is small? 16. A bag of marbles contains 9 large green marbles, 4 large purple marbles, 5 small green marbles, and 4 small yellow marbles. If you draw a marble at random, what is the probability that you will draw a green marble, given that it is large? 17. A jar contains 10 red M&Ms, 13 yellow M&Ms, 7 green M&Ms, 11 blue M&Ms, and 8 brown M&Ms. What is the probability of pulling a brown M&M, replacing in the jar, and then pulling a red M&M? 18. A jar contains 20 red M&Ms, 23 yellow M&Ms, 19 green M&Ms, 15 blue M&Ms, and 17 brown M&Ms. What is the probability of pulling a yellow M&M, replacing in the jar, and then pulling a green M&M? 19. On a certain day, the chance of rain in Ventura is 70% and the chance of rain in San José, Costa Rica is 50%. Suppose that the chance of rain in the two cities is independent. What is the probability that is will not rain in either city? 20. A random number generator selects three digits from {0, 1, …, 9}. What is the probability that all three numbers are less than or equal to 4? 21. On a certain day, the chance of rain in Ventura is 40% and the chance of rain in Tibet is 60%. Suppose the chance of rain in the two cities is independent. What is the probability that it will not rain in either city?