If a lopsided die is rolled where Pr[1] = Pr[2] = Pr[3] =1/4, Pr[4] = Pr[5] = Pr[6] =1/12, A=an odd number occurs, B=a number less than 3 occurs, and C=a multiple of two occurs, then find the following;
1. Pr[A or B],
2. Pr[B and C]
3. Pr[A and notC],
4. Are A & B indep.?
If a lopsided die is rolled where Pr[1] = Pr[2] = Pr[3] =1/4, Pr[4] = Pr[5]...
Question 3 Suppose an unfair die is to an unfair die is rolled. Let random variable X indicate the number that the die lands on when rolled taking on the following probability values T 1 2 X Pr(X=> 1 1 .05 1 05 2 .10 3 20 4 40 5 .15 6 .10 A) Find the probability of rolling a 2 or a 6. ilor si s lo sonensyon b el B) Find the probability of rolling a number greater...
7. (3 points) Given a fair 6-sided die. Each time the die is rolled, the probabilities of rolling any of the numbers from 1 to 6 are all equal. 1) If it is rolled once and let A be the event of rolling a number larger than 3 and B be the event of rolling an odd number. What is P(AV B)? 2) If it is rolled three times, what is the probability that the same number shows up in...
suppose a single die is rolled find:a) P(6, given that an odd number is rolled)b) P(5, given that ann odd number is rolled)is a) 0 and b) 1/6
1. Consider a fair four-sided die, with sides 1, 2, 3, and 4, that is rolled twice. For example, "1,4" would indicate 1 was rolled first and then 4 was rolled second a) Write down the possible outcomes, i.e., the sample space. (b) List the outcomes in the following events: Event A: The number 4 came up zero times. Event B: The number 4 came up exactly one time. . Event C: The sum of the two rolls is odd...
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?
A fair die is rolled 10 times. What is the probability that an odd number (1, 3 or 5) will occur less than 3 times? A. .0547 B. .1172 C. .1550 D. .7752 E. .8450
Two dice were rolled. Answer the questions: I) What is the probability that the first die will have a number that is a multiple of 2 as the outcome? (10 points) a. 1/2 b. 1/5 c. 1/6 d. 1/36 e. None of the above II) What is the probability that the first die will have “a number less than 4” as the outcome? (10 points) a. 1/5 b. 1/3 c. 1/6 d. 1/36 e. None of the above III) What...
If a 25- sided fair die that is numbered from 1 to 25 is rolled once, find the probability of getting (a) a number less than 5 or at least 20. Show your work in details. (b) a number less than 5 and at least 20. Show your work in details (c) an even number. Show your work in details (d) an odd number. Show your work in details
The table below shows the results for the sum when two die are rolled Die 1 Die 2 12 3 45 6 1 2 345 67 2 3 456 78 3 4 567 89 4 5 67 8 9 10 5 678 9 10 11 6 7 89 10 1112 1. What is the probability distribution? (Enter the exact values by using fractions. Use as the division bar. Do not use spaces in your answers.) 4 P(z) 10 12 P(z)...
1. A single 6-sided die is rolled. What is the probability of each outcome? What is the probability of rolling an even number? What is the probability of rolling an odd number? 2. Two 6-sided dice are rolled. Write the number of possible of rolling dice that add up to (a) 4, (b) 6 and (c) 8.