Computer Science Engineering (CSE) Exam  >  Computer Science Engineering (CSE) Questions  >  four fair six-sided dice are rolled. the prob... Start Learning for Free
four fair six-sided dice are rolled. the probability that the sum of the results being 22 is x/ 1296 . The value of x is 
    Correct answer is '10'. Can you explain this answer?
    Most Upvoted Answer
    four fair six-sided dice are rolled. the probability that the sum of t...
    Solution:

    To find the probability that the sum of the results of four fair six-sided dice is 22, we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes.

    Step 1: Determining the Total Number of Possible Outcomes
    Each dice has six possible outcomes, ranging from 1 to 6. Since there are four dice, the total number of possible outcomes is 6^4 = 1296.

    Step 2: Determining the Number of Favorable Outcomes
    To have a sum of 22, we need to find combinations of numbers on the four dice that add up to 22.

    Sub-Step 2.1: Determining the Maximum Value on a Dice
    To determine the combinations, we need to find the maximum value that can be rolled on a dice. Since we have four dice, if all four dice show their maximum value, the sum would be 6 * 4 = 24. Therefore, the maximum value on a dice is 6.

    Sub-Step 2.2: Enumerating the Combinations
    We can enumerate the combinations in the following way:
    - Assume the first dice rolls a 1. We need to find combinations on the remaining three dice that add up to 21.
    - Assume the first dice rolls a 2. We need to find combinations on the remaining three dice that add up to 20.
    - ...
    - Assume the first dice rolls a 6. We need to find combinations on the remaining three dice that add up to 16.

    Sub-Step 2.3: Using Recursion to Find Combinations
    To find the combinations, we can use recursion. We start with the first dice and recursively find combinations on the remaining dice that add up to the remaining sum. The base case is when we have only one dice remaining, and the sum should be between 1 and 6 (inclusive). In this case, we have only one favorable outcome.

    Step 3: Calculating the Probability
    The number of favorable outcomes is the sum of the combinations obtained in Step 2. Therefore, the probability is x/1296.

    Step 4: Evaluating x
    To find the value of x, we need to calculate the number of favorable outcomes. Summing up all the combinations obtained in Step 2, we get x = 10.

    Answer: The value of x is 10.
    Free Test
    Community Answer
    four fair six-sided dice are rolled. the probability that the sum of t...
    Here, we have take two 6 and two 5.
    the addition of those =6+6+5+5 =22.
    therefore we can obtain... there is four fair and two 6 and 5 are take respectively
    =4! /(2! *2!) =6 ways (2! is remove in both cases where 6 are swap themselves same as both 5 also)...
    hence =6+4 =10
    Explore Courses for Computer Science Engineering (CSE) exam

    Top Courses for Computer Science Engineering (CSE)

    four fair six-sided dice are rolled. the probability that the sum of the results being 22 is x/ 1296 . The value of x isCorrect answer is '10'. Can you explain this answer?
    Question Description
    four fair six-sided dice are rolled. the probability that the sum of the results being 22 is x/ 1296 . The value of x isCorrect answer is '10'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about four fair six-sided dice are rolled. the probability that the sum of the results being 22 is x/ 1296 . The value of x isCorrect answer is '10'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for four fair six-sided dice are rolled. the probability that the sum of the results being 22 is x/ 1296 . The value of x isCorrect answer is '10'. Can you explain this answer?.
    Solutions for four fair six-sided dice are rolled. the probability that the sum of the results being 22 is x/ 1296 . The value of x isCorrect answer is '10'. Can you explain this answer? in English & in Hindi are available as part of our courses for Computer Science Engineering (CSE). Download more important topics, notes, lectures and mock test series for Computer Science Engineering (CSE) Exam by signing up for free.
    Here you can find the meaning of four fair six-sided dice are rolled. the probability that the sum of the results being 22 is x/ 1296 . The value of x isCorrect answer is '10'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of four fair six-sided dice are rolled. the probability that the sum of the results being 22 is x/ 1296 . The value of x isCorrect answer is '10'. Can you explain this answer?, a detailed solution for four fair six-sided dice are rolled. the probability that the sum of the results being 22 is x/ 1296 . The value of x isCorrect answer is '10'. Can you explain this answer? has been provided alongside types of four fair six-sided dice are rolled. the probability that the sum of the results being 22 is x/ 1296 . The value of x isCorrect answer is '10'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice four fair six-sided dice are rolled. the probability that the sum of the results being 22 is x/ 1296 . The value of x isCorrect answer is '10'. Can you explain this answer? tests, examples and also practice Computer Science Engineering (CSE) tests.
    Explore Courses for Computer Science Engineering (CSE) exam

    Top Courses for Computer Science Engineering (CSE)

    Explore Courses
    Signup for Free!
    Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
    10M+ students study on EduRev