Math 3301, 3 Pages 5 Exercises lie. Assume all onsider the experiment of rolling a six-sided...
Probability Experiment In Exercises 51-54, a probability experimen consists of rolling a six-sided die and spinning the spinner shown at the left. The spinner is equally likely to land on each color. Use a tree diagram to find the probability of the event. Then tell whether the event can be considered 51. Event A: rolling a 5 and the spinner landing on blue 52. Event B: rolling an odd number and the spinner landing on green 53. Event C: rolling...
Problem 5. A lopsided six-sided die is rolled repeatedly, with each roll being independent. The probabil- ity of rolling the value i is Pi, i = 1, … ,6. Let Xn denote the number of distinct values that appear in n rolls. (a) Find E|X, and E21 (b) What is the probability that in the n rolls of the dice, for n 2 3, a 1, 2, and 3 are each rolled at least once?
You are conducting an experiment while utilizing a six-sided die that does not produce any sort of bias towards any of the 6 numbers. You will roll this die until you achieve the number "six." A.) What is the probability that you have to roll n times? That is, you fail to roll a "six" n-1 times, then roll a six on the nth roll. B.) Sum all of the probabilities from part A. What is the significance of this...
1. A casino wants to see if a six-sided die is fair. They perform an experiment in which they roll the die 100 times and count the number of times the result is a 3. (a) Is this a one or two-sided test? Explain your answer in a complete sentence. (b) Set up the hypotheses for this test both in words and in terms the parameter p which denotes the theoretical probability for getting a roll of the die giving...
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A normal six-sided die has the following (discrete) probabilities: Number Probability 1 1/6 1/6 1/6 1/6 1/6 1/6 What is the expected value of a single roll of the die? 3.5 What is the variance of a single roll of the die? What is the average of the numbers on the die? 3.5 A six-sided die is rigged to have the following probabilities: Number Probability 0.05 0.09...
Consider the experiment of rolling six 6-sided dice. The sample space S is all length-6 sequences made up of integers 1 to 6, with replacement. (a) Find the probability of all dice yielding the same number. (b) Find the probability that all the numbers are distinct.
For the two six-sided dice case: Write out the six-by-six matrix showing all possible (36) combinations of outcomes. Draw a histogram of the probability of outcomes for the dice totals. Explain the shape of the histogram. Draw a Venn diagram for the 36 dice roll combinations. Define a set "A" as all the combinations that total seven; define set "B" as all the combinations that have one die roll (either die 1 or 2) equal to 2. Indicate the sets...
For questions 7 - 12, consider the experiment of rolling a six-sided die once and recording the outcome. This is a standard die - each of the six sides of the die contains a different number from the set of numbers {1, 2, 3, 4, 5, 6}. 7. Define event A = {1, 2} and event B = {2, 4, 5}. What is A B? (a) {1, 2, 4, 5} (b) {2} (c) {1, 2, 2, 4, 5} (d)...
1. A standard six-sided die is rolled. What is the probability of rolling a number greater than 3? Express your answer as a simplified fraction or a decimal rounded to four decimal places. Answer: ____________________ 2. A box contains 48 red marbles, 53 white marbles, and 67 blue marbles. If a marble is randomly selected from the box, what is the probability that it is blue? Express your answer as a simplified fraction or a decimal rounded to four decimal...
2. Let's now use Excel to simulate rolling two 6-sided dice and finding the minimum of both dice. • Create a new Excel sheet in your document. Click on cell Al, then click on the function icon f. and select Math&Trig, then select RANDBETWEEN. In the dialog box, enter 1 for bottom and enter 6 for top. • After getting the random number in the first cell, click and hold down the mouse button to drag the lower right corner...