Week 4 Assignment: Evaluating Probability with the Binomial Distribution
Boris is taking a quiz for an online class. For the quiz, the system randomly
... [Show More] 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.
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.
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.
x
P(X = x)
0
3/16
1
3/8
2
1/16
3
1/16
4
5/16
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.
x
P(X = x)
0
1/20
1
1/10
2
1/10
3
1/4
4
1/10
5
2/5
Which of the following tables shows a valid probability density function? Select all correct answers.
Select all that apply:
Remember that a valid probability density function has all of its probabilities between 0 and 1, inclusive, and the sum of the probabilities equal 1.
A random variable is a variable that is subject to change due to chance in events. It describes the outcomes of a statistical experiment, and it can take on a set of different possible
values. Each random variable value can vary with each repetition of an experiment, and each one has an associated probability (in contrast to other mathematical variables).
Notation for a random variable is an upper case letter, usually X or Y. These variables are usually represented with words, and do not have numerical values. (i.e. "The random variable X represents the number of blue cars on the highway.") Lower case letters like x or y denote the value of a random variable, and x is given as the numerical value of the random variable. (i.e. for x=3, the problem might say that there were 3 blue cars on the highway)
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.
*Notice: X represents a variable in words, and the lower case x is the numerical set of all possible outcomes. For this example, the x values are countable outcomes. Recall that discrete data are data that you can count. So, because you can count the possible values that X can have, and the outcomes are random, X is a discrete random variable. [Show Less]