3. You have a regular deck of 52 playing cards (13 hearts, 13 diamonds, 13 clubs, 13 spades). If the deck has been well-shuffled and you are dealt one card from the top, answer these probability questions. Note: Final answers should be written out to 3 decimals places, after rounding. For example, if your final answer is 0.1234, then enter 0.123. If your answer is 0.1235, then enter 0.124. Accepted characters: numbers, decimal point markers, sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form fa + bi} where "a" and "b" need to have explicitly stated values. For example: {1+1i) is valid whereas (1+i) is not. {0+9} is valid whereas (9i} is not. a. What is the probability that the suit of the card will be heart or diamond? b. What is the probability that the card will be a heart or will be the number 9? c. If you also flip an ordinary two-sided (Le. "heads" and "tails") coin, what is the probability that the coin will be "heads" up and the card will be a 7 of spades? 4. Casino Probabilities The floor manager of a casino brings a single die to you. He believes that the die is suspicious because it appears to roll central values like 3 or 4 much more frequently than the more extreme numbers like 1 or 6. He suspects that his die has been modified, and wants you to test it. You roll the manager's die 1,200 times and get the following results. Number Relative Frequency of the Number 1/12 1/12 3 1/3 1/3 1/12 6 1/12 Note: Final answers should be written out to 3 decimals places, after rounding. For example, if your final answer is 0.1234, then enter 0. 123. If your answer is 0. 1235, then enter 0.124. a. Consider a perfect die in which each number is equally likely. If a player rolls the perfect die, what is the probability she/he will get any one of these numbers (2, 3, 4 or 5)? b. What is the probability of getting any one of these numbers (2, 3, 4 or 5) if a player rolls the manager's suspicious die