Four fair eight-sided dice are rolled. An outcome is an ordered sequence of 4 numbers between 1 and 8. For example, the sequence 1-1-4-3 is different fromthe sequence 4-1-3-1.a) How many outcomes are possible?b) What is the probability that a roll results in 4 different numbers?c) What is the probability that a roll results in 4 of the same number?a) The number of possible outcomes is(Simplify your answer.)b) The probability that a roll results in 4 different numbers is(Type an integer or decimal rounded to four decimal places as needed.)c) The probability that a roll results in 4 of the same number is(Type an integer or decimal rounded to seven decimal places as needed.)

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Answered: Four fair eight-sided dice are rolled.…

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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A group consists of four Democrats and five Republicans. Four people are selected to attend a conference. a. In how many ways can four people be selected from this group of nine? b. In how many ways can four Republicans be selected from the five Republicans? c. Find the probability that the selected group will consist of all Republicans.
A child is playing with number blocks. She has nine blocks, numbered 1 through 9. a) If she selects three blocks at random from the nine blocks and puts them to the side, what is the probability that she selects the 1, 2, and the 3? b) If she selects three blocks at random from the nine blocks, and lines them up to make a three digit number, how many possible three-digit numbers are there?
Topic: Choosing ping-pong balls without replacement.There are 6 white and 4 orange ping-pong balls in a brown paper bag. Two balls are randomly chosen.Enter your answers as fractions. (The "Preview" simply displays your answer in nice mathematical text.It does not mean that your answer is either right or wrong.)a) How many total balls are in the bag? b) What is the probability that the 1st ball is orange?P(1st = orange) = c) What is the probability that the 2nd ball is also orange, given that the 1st ball was orange?P(2nd = orange | 1st = orange) = d) What is the probability that both the 1st and the 2nd balls are orange?
Keno is a casino game in which the player has a card with the numbers 1 through 80 on it. The player selects a set of k numbers from the card, where k can range from one to ifteen. The “caller” announces twenty winning numbers, chosen at random from the eighty. The amount won depends on how many of the called numbers match those the player chose. Suppose the player picks ten numbers. What is the probability that among those ten are six winning numbers?
You randomly select an integer from 0 to 9 (inclusively) and then randomly select an integer from 0 to 19 (inclusively). What is the probability of selecting a 7 both times? The probability is enter your response here. (Type an integer or a decimal. Do not round.)
Part 2: Finding Probability Find the probability (in fraction form) for each given situation. A single die is rolled. What is the probability of rolling... a) the number 4 b) an even number c) a number greater than 2 Two dice are rolled at the same time. What is the chance of getting. a) two even numbers b) a sum of 12 c) a sum of 7 d) doubles Flipping a quarter three times. What is the chance of getting (in order) a) heads, tails, heads (HTH) b) two heads in any order c) tails all three times
A bag contains 9 marbles: 2 are green 5 are red and 2 are blue. Bob chooses a marble at random and without putting it back choose another one at random. What is the probability that the first marble is green and the second is red? Write your answer as a fraction in simplest form.
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A coin is tossed three times. An outcome is represented by a string of the sort HTT (meaning heads on the first toss, followed by two tails). The 8 outcomes are listed below. Assume that each outcome has the same probability. Complete the following. Write your answers as fractions. (a)Check the outcomes for each of the three events below. Then, enter the probability of each event. Outcomes Probability HHH HHT HTH HTT THH THT TTH TTT Event A: The first toss is heads Event B: More heads than tails Event A and B: The first toss is heads and more heads than tails (b)Suppose the first toss is heads. (That is, Event A occurs.) This will limit the possible outcomes. From the remaining outcomes, check the outcomes for Event B . Then, enter the probability that Event B occurs given…
In a lottery, the top cash prize was $659 million, going to three lucky winners. Players pick five different numbers from 1 to 57 and one number from 1 to 42. A player wins a minimum award of $450 by correctly matching three numbers drawn from the white balls (1 through 57) and matching the number on the gold ball (1 through 42) What is the probability of winning the minimum award? The probability of winning the minimum award is (Type an integer or a simplified fraction.)
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