Problem 3. (10 points) We roll two fair 6-sided dice. (1) What is the probability that...
We roll two fair 6-sided dice. (1) What is the probability that at least one die roll is 6? (2) Given that two two dice land on different numbers, what is the conditional probability that at least one die roll is a 6? Thint] You may use the graphical approach (Lecture 5 slide 11-12) to help you solve the problem. Problem 4. (8 points) We deal from a well-shuffled 52-card deck. What is the probability that the 13th card is...
8. We roll two fair dice. (1) Given that the roll results in a sum of 6 or less, what is the conditional probability that doubles are rolled? A "double" means that two dice have the same number (2) Given that the two dice land on different numbers, what is the conditional proba- bility that at least one die roll is a 1?
Problem #3: 5 fair 12-sided dice are rolled. (a) [3 marks] Find the conditional probability that at least one die lands on 3 given that all 5 dice land on different numbers. 6) [2 marks] True or False: If X is the maximum of the 5 numbers from one roll, and Y is the minimum of the 5 numbers from one roll, then X and Y are independent random variables.
Find the conditional probability, in a single roll of two fair 6-sided dice, that neither die is a three, given that the sum is greater than 6 7 The probability is 12 (Type an integer or a simplified fraction)
If we roll a red 6-sided die and a green 6-sided die (both are fair dice with the numbers 1-6 equally likely to be rolled), what is the probability that we get (i) A 5 on the green die AND a 3 on the red die? (ii) A 5 on the green die OR a 3 on the red die? (iii) A 5 on the green die GIVEN we rolled a 3 on the red die?
A) Suppose I roll two fair six-sided dice. What is the probability that I rolled a total of 5? B) Suppose I roll two fair six-sided die and I announce that the sum of the two die is 6 or less. What is the probability that I rolled a total of 5?
Problem 1 (10 points). If two fair dice are rolled 10 times, what is the probability of at least one 6 (on either die) in exactly five of these 10 rolls? (Hint: For each roll, two dice are rolled at the same time. It is considered as the success if at least one of two dice is 6 and as the failure if neither of dice is 6.]
Find the conditional probability, in a single roll of two fair 6-sided dice, that the sum is less than 6, given that the sum is even The probability is 2 (Type an integer or a simplified fraction) 1
1. We roll two fair 6-sided dice. Compute the probabilities of the following events. (a) The sum is at most 6. (b) The sum is more than 6. (c) The sum is at most 6 and at least one die is a 4. 2. Consider the letters a,b,c. Suppose we draw 2 of the letters at random (allowing for repetition). Assume order matters. That is, ab is not the same as ba: Let A : The 2 letters are distinct....
1.) Suppose you roll two fair six-sided dice. What is the probabilty that I rolled a total of 5? 2.) Suppose you roll two fair six-sided die and I announce that the sun of the two die is 6 or less. What is the probabilty that you rolled a total of 5?