What is the probability of getting a total of 6 when three dice are thrown simultaneously?
Three dice are thrown simultaneously. Find the probability of getting a number on at least one die equal to even prime number.
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Answer (Detailed Solution Below)Option 2 : 91/216
 Free Child Development and Pedagogy Mock Test 10 Questions 10 Marks 10 Mins Given: Three dice are thrown simultaneously. Concepts used: A fair die is numbered from 1 to 6 with probability of coming of each number being 1/6. Total number of outcomes on roll of three dice = 216 Calculation: Even prime numbers out of 1 to 6 is 2. ⇒ Probability of getting number of outcomes in which even prime number appears on at least one die = P (Number of outcomes in which 2 appears on one die + Number of outcomes in which 2 appears on two dice + Number of outcomes in which 2 appears on three dice) ⇒ P (Number of outcomes in which even prime number appears on at least one die) = P {(3 × 1/6 × 5/6 × 5/6)} + P {(3 × 1/6 × 1/6 × 5/6)} + P {(1/6 × 1/6 × 1/6)} = 91/216 ∴ Probability of getting a number on at least one die equal to even prime number is 91/216. Alternative solution: The only even prime number out of 6 numbers (1, 2, 3, 4, 5, 6) is 2. ⇒ P (2 comes on at least one die) = 1 - P (2 comes on neither die) ⇒ P (2 comes up on at least one die) = 1 - (5/6 × 5/6 × 5/6) ⇒ P (2 comes up on at least one die) = 91/216. ∴ Probability of getting a number on at least one die equal to even prime number is 91/216. Last updated on Sep 22, 2022 Application deadline for HTET 2022 extended. The candidates can now apply online till 30th September 2022. The exam is conducted by the Board of School Education, Haryana to shortlist eligible candidates for PGT and TGT posts in Government schools across Haryana. The exam is conducted for 150 marks. The HTET Exam Pattern for Level I, Level II, and Level III exams is different. There will be no negative marking in the exam. $\begingroup$ I am having a hard time wrapping my head around this and am sure that my answers are wrong. There are three dice. A. Chance of getting exactly one six on the three dice. $$(1/6) * 3 = 1/3$$ B. Chance of getting exactly two sixes. $$(1/6 * 1/6) * 1.5 = 1/24$$ C. Chance of getting exactly $~3~$ sixes. $$1/6 * 1/6 * 1/6 = 1/216$$ D. Chance of any combination of A, B and C $$1/3 + 1/24 + 1/216= 72/216 + 9/216 + 1/216 = 82/216$$
nmasanta 8,82125 gold badges23 silver badges47 bronze badges asked Oct 14, 2013 at 9:04
$\endgroup$ 1 $\begingroup$ A. There is a total of 6^3=216 combinations if you roll 3 dice. There are 5^2x3=75 combinations that you will get one 6. Thus there is a 75/216=25/72 chance of getting only one 6 when rolling 3 dice. B. There are 5x3 combinations that you will get 2 6s. Thus there is a 15/216=5/72 chance of getting a 2 6s when rolling 3 dice. C. There is 1 combination where you will get 3 6s. Thus there is a 1/216 chance you will get 3 6s when rolling 3 dice. (Good job you got this correct) D. There is a 75+15+1/216=91/216 chance of any of them happening. answered Oct 14, 2013 at 9:41
EpicGuyEpicGuy 2731 silver badge9 bronze badges $\endgroup$ 4 $\begingroup$ Hint for A: what is the chance that no sixes appear? If you know that chance then you automatically know the chance that sixes do appear. answered Oct 14, 2013 at 9:13
drhabdrhab 143k10 gold badges71 silver badges192 bronze badges $\endgroup$ $\begingroup$ The chance of getting at least one 6 with three dice is 91/216 because if you subtract 125/216 (the probability of rolling three dice without getting a 6) from 216/216 (the probability of any combination of numbers), you get 91/216.
answered Nov 26, 2013 at 16:09
user111236user111236 821 silver badge5 bronze badges $\endgroup$ 1 What is probability of getting a sum of 6 if we throw 3 dice together?Possibility of getting a sum of 6: 10/216 = 0.0462 × 100 = 4.6% Possibility of getting a sum of 7: 15/216 = 0.069 × 100 = 7.0% Possibility of getting a sum of 8: 21/216 = 0.097 × 100 = 9.7%
What is the probability of getting 6 when a dice is tossed once?The probability of getting number 6 in a throw of a dice is 1/6Similarly, the probability of getting a number 5 is 1/5.
What is the probability of 3 dice?The three dice are rolled fairly without any cheating. Each of the dice rolls is an Independent Event, that is the outcome from anyone dice roll has no impact whatsoever on the outcome of any other dice roll. The probability of all three happening is the product of the three probabilities: 1 × (1/6) × (1/6) = 1/36.
What is the number of outcomes of the sum of three 6 sided dice?Solution: Three different dice are thrown at the same time. Therefore, total number of possible outcomes will be 63 = (6 × 6 × 6) = 216. i.e. (1, 1, 1), (1, 1, 2), (1, 2, 1), (2, 1, 1), (1, 1, 3), (1, 3, 1), (3, 1, 1), (2, 2, 1) and (1, 2, 2).
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