(2) Three dice are rolled. If each lands on a different number, find the probability that one is 3. (2) Three dice are rolled. If each lands on a different number, find the probability that one...
1) Three dice are rolled. If each lands on a different number, find the probability that one is 3? 2) ) Three machines (A, B, C) manufacture screws. They manufacture 25%, 35%, and 40% of the screws, respectively. The output screws are defective at 2%, 3%, and 5%, respectively. If you choose a random screw produced at the factory and it is defective, what is the probability it came from each machine A, B, and C
3 Dice are rolled, what is the probability that they are all different numbers and one of them lands on a 6?
If two fair dice are rolled, what is the conditional probability that the rst one lands on an even number given that the second one lands on a number less than or equal to four? Compute the conditional probability that the second one lands on a number less than four given that the rst one lands on an even number.
If two fair dice are rolled, what is the conditional probability that the first one lands on 6 given that the sum of the dice is i? Compute for all i = 2, 3, . . . , 12.
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.
b) A loaded dice never lands showing the number 2, lands showing 6 with probability 1/3, and all other numbers with probability 1/6. i) Calculate the probability that 3 such loaded dice land showing the same number 4 marks] Calculate the probability that when one such loaded dice is thrown together 3 marks] ii) with a fair dice they land showing the same number. c) The mean free path of a hydrogen molecule in air is 110 nm at standard...
4. Three fair dice have different colors: red, blue, and yellow. These three dice are rolled and the face value of each is recorded as R, B, Y, respectively. (a) Compute the probability that B< Y < R, given all the numbers are different; (b) Compute the probability that B< Y< R.
Two dice are rolled one after the other. Find the probability that the sum of the dots on the dice total is a number greater than 11 if the second die is a 5
Suppose three dice are rolled. Each die is equally likely to take values between 1 and 6, inclusive. Given that all three dice have different values. Find the probability that the smallest value of the three dice is 2.
Three fair dice, each has 6 different faces, are rolled. Let B define the event that no two or no three dice show the same face. What is the probability of B