Question 6 3 pts Exercise f. Consider the experiment in which three fair (and independent) dice...
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?
You roll a pair of fair 6-sided dice: a red die and a blue die. (a) Consider event A: {the outcome of the red die is more than 3} and event B: {the outcome of the red die is less than 5}. Given that event A occurs, what is the probability that event B occurs? (b) Are A and B mutually exclusive (i.e., disjoint)? (c) Are A and B independent? (d) Calculate the probability of event C: {the outcome of...
You roll a pair of fair 6-sided dice: a red die and a blue die. (a) Consider event A: {the outcome of the red die is more than 3} and event B: {the outcome of the red die is less than 5}. Given that event A occurs, what is the probability that event B occurs? (b) Are A and B mutually exclusive (i.e., disjoint)? (c) Are A and B independent? (d) Calculate the probability of event C: {the outcome of...
1. A blue fair 6-sided dice and a red fair 6-sided dice are rolled at the same time. a) What is the probability of the sum of the dice equals 7, given 1 2 3 4 5 6 at least one of the dice shows a 3? 1 (1.1) (1.2) (1.3) (1.4) (1.5) (1.6) 2 (2.1) (2.2) (2.3) (2.4) (2.5) (2.6) (3.1) (3.2) (3.3) (3.4) (3.5) (3.6) (4.1) (4.2) (4.3) (4.4) (4.5) (4.6) 5 (5.1) (5.2) (5.3) (5.4) (5.5) (5.6)...
Two fair six-sided dice are rolled. What is the probability that one die shows exactly three more than the other die (for example, rolling a 1 and 4, or rolling a 6 and a 3)
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.
Three fair six-sided dice are rolled. a) What is the probability of seeing {1, 3, 6}? b) What is the probability of seeing {1, 4, 4}? c) What is the probability of seeing {2, 2, 2} ? d) What is the probability of seeing at least one 6? e) What is the probability that the sum of all three dice is 16? f) What is the probability of seeing exactly two even numbers?
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)
Question 3 3 pts Matching problem [Choose] You roll a fair six-sided die 500 times and observe a 3 on 90 of the 500 rolls. You estimate the probability of rolling a 3 to be 0.18 Choose) You roll a fair six-sided die 10 times and observe a 3 on all 10 rolls. You bet the probability of rolling a 3 on the next rollis close to O since you have already had 10 3's in a row You assign...
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....