Question: Question 2. Consider a scenario in which you roll two 6sided dice. (a) If the dice are fair, what is the probability that you get

Question 2. Consider a scenario in which you roll two 6sided dice. (a) If the dice are fair, what is the probability that you get a sum that is less than 5? (b) If the dice are fair, what is the probability that you get a sum that is a perfect square? (c) If the dice are fair, what is the probability that you get a sum that is less than 4 or greater than 6? (d) If the dice are both weighted so that even numbers occur twice as often as odd numbers, what is the probability that you get an even sum? Question 3. Consider a scenario in which you roll a die 5 times in a row. (a) If the die is fair, what is the probability that you get exactly two 2's? (b) If the die is fair, what is the probability that you get exactly two even numbers? (0) If the die is fair, What is the probability that you get a different number each time? (d) If the die is fair, what is the probability that the last two rolls are less than 3 given that the rst two rolls were greater than 3? Are these two events independent? Explain your answer. (e) If the die is fair, what is the probability that you roll at least 4 even numbers given that the rst two rolls are even? Are these two events independent? Explain your answer. (f) Answer (a) and (b) again for a die that is weighted so that even numbers are rolled twice as often as odd numbers. Question 4. Consider a scenario where you are dealt a 7-card hand from a regular 52-card deck. (a) What is the probability that all 7 cards are the same suit? (b) What is the probability that the hand is in the form XXYYZZA? (c) What is the probability that you get exactly two Queens or two Kings? ((1) What is the probability that the hand is of the form ABCDEFG? (e) What is the probability that the hand contains 4 hearts and 3 diamonds? (f) What is the probability that the hand contains 4 hearts and 3 diamonds given that the hand is all red? Are these events independent? Explain your

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