Week 3 – Probability Distributions
38632. Suppose that Bob and Sarah are married. Bob’s family is from New York. Sarah’s family is from Los Angeles. Both families have invited them to spend New Year’s Eve with them. Due to distance, they can only go to one place, and to make the decision fair, they are going to randomly draw a card from a deck of cards. If it is red (hearts or diamonds), then they will go to Sarah’s family. If it is black (clubs or spades), they will go to Bob’s family. Let’s say they repeated this process for the 4th of July, Thanksgiving, and Christmas. Draw a tree diagram depicting the sample space outcomes for this experiment showing all the possible outcomes for the card draws. Use R for a red card and B for a black card. Note: the card is always replaced after drawing. Most students draw this an upload or embed the picture. (Make sure you understand what sample space is before doing this).
2. Explain if each card draw in the scenario in #1 is an example of a mutually exclusive event or not.
3. Explain if each card draw in the scenario in #1 is an independent event or not.
4. Classify each of the following random variables as discrete or continuous in the scenario in #1.
a. X = the number of times you draw a card from a deck
b. X = the temperature in the room you are playing cards in
c. x = how many people you are playing cards with
d. x = how much time it take you to shuffle a deck of cards
5. List and explain the characteristics of a binomial experiment. It’s the explanation that is worth the most point here. After each characteristic (and there should be at least 4), explain it.
6. Read this scenario keeping in mind what you just wrote in #5:
Jason is the father in the Smith family. His favorite ice cream place is just up the street. He treats himself to an ice cream cone every Friday night. He is equally likely to choose either vanilla venom or caramel crush (the two best flavors ever created). In fact, he loves both flavors so much that he flips a coin to determine which one to get in his 52 trips during a year. If he flips a heads, he orders vanilla venom. If he flips a tails, he orders caramel crush. His wife is happy when the coin toss results in the vanilla venom because Jason is a messy eater, and that flavor is easier to successfully wash out of the shirt. It’s a success when his shirt is not ruined.
Then, thoroughly explain whether the following are true or false.
a. This experiment has 2 trials.
b. The success is flipping a tails.
c. The probability of success in all trials is 1/2.
d. The coin toss ensures that the trials are independent and mutually exclusive.
e. This scenario is an example of a binomial experiment.
f. This probability of success remains the same throughout the experiment.
g. The experiment has a fixed number of trials.
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