In an experiment with throwing 2 fair dice, consider the events A : The sum of numbers on the faces is 8 B : Doubles are thrown. What is the probability of getting A or B ?
Answer :
Total outcomes for rolling 2 die = 36
Outcomes in event A = {(2,6) (3,5) (4,4) (5,3) (6,2) }
N(A) =5
Outcomes of event B = {(1,1) (2,2) (3,3) (4,4) (5,5) (6,6) }
A union B = { (1,1) (2,2) (3,3) (4,4) (5,5) (6,6) (2,6) (3,5) (5,3) (6,2)}
Probability of A or B = n(A union B)/36 = 10/36 = 5/18
In an experiment with throwing 2 fair dice, consider the events A : The sum of...
Part I - Throwing a Dice with Six Faces (32 points) Consider a dice with six faces, i.e. a standard dice. The possible outcomes after throwing the dice once are 1, 2,3, 4,5,6 (a) Assume that the dice is thrown once. Let w represents the outcome. Explain why P(w-i) for i = i..6, when the dice is fair (b) The fair dice is thrown twice. Find the probability of occurance of at least one 6 The fair dice is thrown...
3) We roll 2 fair dice. a) Find the probabilities of getting each possible sum (i.e. find Pr(2), Pr(3), . Pr(12) ) b) Find the probability of getting a sum of 3 or 4 (i.e.find Pr(3 or 4)) c) Find the probability we roll doubles (both dice show the same value). d) Find the probability that we roll a sum of 8 or doubles (both dice show the same value). e) Is it more likely that we get a sum...
.1. A pair of fair dice is thrown, what is the probability that the sum of the two numbers is greater than 10. 2. A pair of fair dice is thrown. Find the probability that the sum is 9 or greater if a. If a 6 appears on the first die. b. If a 6 appears on at least one of the dice.
E B Prutent laut ya ne. Example 3. Suppose you are throwing two fair dice. a) What is the probability that you will roll a sum less than four or bigger than 10? Howy beck b) What is the probability that you will roll doubles or a sum bigger than 10?
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?
An experiment is rolling two fair dice. (a) Describe the Sample Space. How many outcomes are there? (b) Compute the probability of getting a sum of 7. (c) Compute the probability of getting the first die is a 4. (d) Compute the probability of getting a sum of 7 OR the first die is a 4. (Hint: What rule deals with finding “OR” probabilities?) (e) Compute the probability of NOT getting a sum of 7.
2) Two fair dice are rolled. Find the following probabilities: (10pts) a) P(the sum of the dice is not eight) b) P(doubles are rolled) c) P(doubles are rolled given that the sum of the dice is eight)
Consider two fair, FOUR sided dice, with faces labeled 1, 2, 3, 4. Compute the probability of rolling a) a sum of 3 b) a sum of 6 c) a sum of 9 d) the most likely sum(s) along with its probability.
Passedix is a game of chance played with three fair dice. Players bet whether the sum of the faces shown on the dice will be above or below ten. During the late sixteenth century, the astronomer and mathematician Galileo Galilei was asked by the Grand Duke of Tuscany to explain why “the chance of throwing a 9 with three fair dice was less than that of throwing a 10.” (Interstat, Jan. 2004) The grand duke believed that the chance should...
Consider the experiment of rolling two dice. a) What is the probability of obtaining a sum of five? b) What is the probability of obtaining a sum of four or less? c) What is the probability of obtaining a sum of eight or more? a) The probability of obtaining a sum of five? . (Type an integer or a simplified fraction.)