MATH 225N Week 4 Assignment; Evaluating Probability With The Binomial Distribution

Institution	MATH 225N Statistical Reasoning for the Health Sciences
Contributor	Brianna

Question: Boris is taking a quiz for an online class. For the quiz, the system randomly assigns 2 high-difficulty questions, 7 moderate-difficulty questions, and 6 low-difficulty questions. What is the probability that Boris is assigned a moderate-difficulty question first? Give your answer as a fraction.
Question: A baker finds several new recipes to try. Of the new recipes, there are 11 for cookies, 10 for muffins, and 4 for cakes. If the baker selects a recipe at random, what is the probability the recipe is for a cake? Give your answer as a fraction.
Question: The table below shows a probability density function for the discrete random variable X, the number of times students had to retake a math test until they received a perfect score. What is the probability that X is 0 or 2? Provide the final answer as a fraction.
Question: The table below shows a probability density function for a discrete random variable X. What is the probability that X is 0, 3, or 5? Provide the final answer as a fraction.
Question: Which of the following tables shows a valid probability density function? Select all correct answers. Select all that apply:

Example

You are flipping three fair coins, and want to know the possible outcomes.
Let the random variable X = the number of heads you get when you toss three fair coins.
The sample space (possible outcomes) for the toss of three fair coins is TTT, THH, HTH, HHT, HTT, THT, TTH, HHH. (H = heads; T = tails)
So, x = 0,1,2,3, because when you toss three coins, you have the possibility of getting 0 heads, 1 head, 2 heads, or 3 heads.