(4) Consider a roll of six dice of different colors.(a) How many different rolls are possible? (Assume the colors of the dice arerelevant for distinguishing between rolls.)(b) How many different rolls have at least one 1 appear among the six dice?(c) How many different rolls have at least one 1 or at least one 5 among the sixdice?

Six dice of different colors are rolled.

Answered: (4) Consider a roll of six dice of…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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9 A bag contains 12 red and 8 blue balls that are identical except for their colour. A ball is chosen from the bag, its colour noted, and then it is replaced. Eight balls are chosen. (i) Find (a) the probability of obtaining five red balls (b) the probability of obtaining at least two blue balls (c) the probability of obtaining equal numbers of red and blue balls. (ii) How many balls need to be chosen if the probability of obtaining at least one red ball is to be at least 99%?
Question 4-Rolling of two dice Here are some warm-up questions: a) What are the possible values that can show up when adding the dots of two dice? b) Are there an equal number of odd and even values among the sums you listed in part a)? c) Are all the values listed in part a) equally likely? Or are some more likely than others? d) Start by thinking about the different ways you can make a sum of 6. What should be the probability of rolling a sum of 6? e) To analyze this problem, you need to find all possible outcomes of rolling two dice. We can organize these possible rolls in a table. It is helpful to think about the two dice having different colors. Fill in the table on the right with the sum of the spots for each of the pairs above. One value is filled in: 4 + 3 = 7. 1 5 6 1 4 7 C f) Use the table on the right to compute what the probability is for rolling an even sum, and what the probability is for rolling an odd sum. Mark the even sums in the table above. P(even sum) P(odd sum)=…
Consider the experiment where two fair six-sided dice are rolled and their face values recorded.a) Given the following events: A = {(3, 5)}B = a 4 is rolled on the first dieC = a 5 is rolled on the second dieD = the sum of the dice is 7E = {(7,4)} Find the following:i. B ∩ D and B ∪ D ∪ A ∩ C′ii. A ∩ D and A ∪ D′ ∩ B
Parts 4 and 5 please
I get to draw two buttons from a bag with 3 Cardinal and 6 Gold buttons (without replacement, order does not matter).What is the probability that I get one of each color? a. 1/2 b. 5/9 c. 4/9 d. 1/3 e. None of the other answers is correct.
A coin is tossed three times, where (i) A: head on third toss, B: heads on first two tosses (ii) A: at least two heads, B: at most two heads (iii) A: at most two tails, B: at least one tail In each case find P(A/B).
1.) A basket contains 11 red apples and 8 green apples. A sample of 5 apples is drawn. Find the probability that the sample contains the following, and give your answer as a reduced fraction. (a) All green apples (b) 2 green apples and 3 red apples (c) More red than green apples
Macrostates, Microstates, and Probabilities ) Macrostates and Microstates: 1) Suppose we flip n = 2 coins at the same time. If we are interested in how many heads we might get, then we can define a macrostate by just naming N = the number of heads. How many possible macrostates are there when you flip 2 coins? 2) Now we count the total number of different possible ways the coins can land when we toss two coins. We call these "possible ways" microstates. For our two coin toss, list all the possible microstates.
An experiment involves 32 participants. From these, a group of 5 participants is to be tested under a special condition. How many groups of 5 participants are possible? (b) From a collection of 51 store customers, 2 are to be chosen to receive a special gift. How many groups of 2 customers are possible?
counting techniques and probability - Statistics and probability 1) A friend of mine is going to offer a party. His current stock of wine includes 8 bottles of Zinfandel, 10 of Merlot, and 12 of Cabernet (he only drinks red wine), all from different wineries. a) If 6 bottles are selected at random, what is the probability that the result will be two bottles of each? variety? b) If 6 bottles are chosen at random, what is the probability that all of them are of the same variety?
1. If a die is rolled, find out the following: (i) The probability of getting an even number (ii) The probability of getting a 4 2. If two dice are rolled, then find out the following: (i) The probability that the sum is equal to 9 (ii) The probability that the sum is equal to 7 If a card is drawn at random from a pack of 52 cards, then find out the following: (1) P(Ace or Red) (ii) P(Non Black or Ace) 3. 4. A Jar contains 3 red, 4 green and 3 blue balls. If two balls are chosen at random from the Jar, Find out the following: (i) The probability that they are red or green. (ii) The probability that they are blue or red. 5. If three coins are tossed, then find out the following- (i) Probability of getting two tails (ii) Probability of getting three heads 6. Of the cars on a used car lot, 70% have CD player (CD) and 30% have air conditioning (AC). 10% of the cars have both. (i) What is the probability that a car has 'No AC', given that it has 'CD'? (ii) What is the probability that a car…
4.) Find the probability of getting the following 5-card poker hands. (a) A royal flush (A, K, Q, J, 10 of a single suit.) (b) A straight (5 cards in a row, not all of the same suit, with ace either high or low) c) Three of a kind (exactly 3 cards of the same kind) (d) Exactly 2 different suits

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