Suppose you have a die that has probability p of resulting in the outcome 6 when rolled, where p is a continuous random variable that is uniformly distributed over [0,1/3]. Suppose you start rolling this die. (The value of p does not change once you start rolling.) Give exact answers as simplified fractions.
a) Compute the probability that the first roll is 6.
b) Compute the probability that the first two rolls are both 6.
Suppose you have a die that has probability p of resulting in the outcome 6 when...
Suppose you have a die that has probability p of resulting in the outcome 6 when rolled, where p is a continuous random variable that is uniformly distributed over [O, j]. Suppose you start rolling this die. (The value of p does not change once you start rolling.) Give exact answers as simplified fractions. (a) Compute the probability that the first roll is 6. b) Compute the probability that the first two rolls are both 6. (c) Let Si be...
You have two fair, 6-sided dice. Die 1 has 4 white faces and 2 black faces. Die 2 has 2 white faces and 4 black faces. You roll Die 1. If it comes up white, then Die 1 is the “chosen die” and you put Die 2 away, but if it comes up black, then Die 2 is the “chosen die” and you put Die 1 away. You now roll the chosen die twice, noting the color that comes up...
Suppose I asked you to roll a fair six-sided die 6 times. You have already rolled the die for 5 times and six has not appeared ones. Assuming die rolls are independent, what is the probability that you would get a six in the next roll? 1/6 1/2 5/6 0 1
Please show work :) Will upvote/rate! 3. Discrete Random Variables You have a biased die, where the probability that a number n appears on the die when it is rolled is defined as a random variable X such that Р(X %3D п) — с:п Here c is a positive real number. Now answer the questions below: (a) Find the value of c (b) What is the expected value of the random variable X? (c) Find how close a number you...
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.
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...
This question is due my 11:50pm EST One die is rolled 2 times in a row. The observation is the number that comes up on each roll (rolling 2 and 5 is not the same as rolling 5 and 2). Describe one outcome and find a number of outcomes. Write all outcomes of the sample space S (you can use … notation to indicate many numbers of cases). : “pairs are rolled” (both dice come up the same number) Write...
Suppose you are rolling a fair four-sided die and a fair six-sided die and you are counting the number of ones that come up. What is the probability that both die roll ones? What is the probability that exactly one die rolls a one? What is the probability that neither die rolls a one? What is the expected number of ones? If you did this 1000 times, approximately how many times would you expect that exactly one die would roll...
6. A fair six sided die is rolled three times. Find the probability that () all three rolls are either 5 or 6 (6) all three rolls are even (c) no rolls are 5 (d) at least one roll is 5 (e) the first roll is 3, the second roll is 5 and the third roll is even
Probability calculation: discrete/finite example • Two rolls of a tetrahedral die . Let every possible outcome have probability 1/16 • P(X = 1) = Let 2 = min(X,Y) Y = Second roll • P(Z = 4) = • P(Z = 2) = 1 4 2 3 X = First roll