What is the probability of getting the sum as 9 when three dice are thrown?
Probability for rolling three dice with the six sided dots such as 1, 2, 3, 4, 5 and 6 dots in each (three) dies. Show Worked-out problems involving probability for rolling three dice: 1. Three dice are thrown together. Find the probability of: (i) getting a total of 5 (ii) getting a total of atmost 5 (iii) getting a total of at least 5. (iv) getting a total of 6. (v) getting a total of atmost 6. (vi) getting a total of at least 6. Solution: Three different dice are thrown at the same time. Therefore, total number of possible outcomes will be 63 = (6 × 6 × 6) = 216.(i) getting a total of 5: Number of events of getting a total of 5 = 6 i.e. (1, 1, 3), (1, 3, 1), (3, 1, 1), (2, 2, 1), (2, 1, 2) and (1, 2, 2) Therefore, probability of getting a total of 5 Number of favorable outcomesP(E1) = Total number of possible outcome = 6/216 (ii) getting a total of atmost 5: Number of events of getting a total of atmost 5 = 10 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). Therefore, probability of getting a total of atmost 5 Number of favorable outcomesP(E2) = Total number of possible outcome = 10/216 (iii) getting a total of at least 5: Number of events of getting a total of less than 5 = 4 i.e. (1, 1, 1), (1, 1, 2), (1, 2, 1) and (2, 1, 1). Therefore, probability of getting a total of less than 5 Number of favorable outcomesP(E3) = Total number of possible outcome = 4/216 Therefore, probability of getting a total of at least 5 = 1 - P(getting a total of less than 5) = 1 - 1/54 = (54 - 1)/54 = 53/54 (iv) getting a total of 6: Number of events of getting a total of 6 = 10 i.e. (1, 1, 4), (1, 4, 1), (4, 1, 1), (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), (3, 2, 1) and (2, 2, 2). Therefore, probability of getting a total of 6 Number of favorable outcomesP(E4) = Total number of possible outcome = 10/216 (v) getting a total of atmost 6: Number of events of getting a total of atmost 6 = 20 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), (1, 2, 2), (1, 1, 4), (1, 4, 1), (4, 1, 1), (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), (3, 2, 1) and (2, 2, 2). Therefore, probability of getting a total of atmost 6 Number of favorable outcomesP(E5) = Total number of possible outcome = 20/216 (vi) getting a total of at least 6: Number of events of getting a total of less than 6 (event of getting a total of 3, 4 or 5) = 10 i.e. (1, 1, 1), (1, 1, 2), (1, 2, 1), (2, 1, 1) (1, 1, 3), (1, 3, 1), (3, 1, 1), (1, 2, 2), (2, 1, 2), (2, 2, 1). Therefore, probability of getting a total of less than 6 Number of favorable outcomesP(E6) = Total number of possible outcome = 10/216 Therefore, probability of getting a total of at least 6 = 1 - P(getting a total of less than 6) = 1 - 5/108 = (108 - 5)/108 = 103/108 These examples will help us to solve different types of problems based on probability for rolling three dice. Probability Probability Random Experiments Experimental Probability Events in Probability Empirical Probability Coin Toss Probability Probability of Tossing Two Coins Probability of Tossing Three Coins Complimentary Events Mutually Exclusive Events Mutually Non-Exclusive Events Conditional Probability Theoretical Probability Odds and Probability Playing Cards Probability Probability and Playing Cards Probability for Rolling Two Dice Solved Probability Problems Probability for Rolling Three Dice 9th Grade Math From Probability for Rolling Three Dice to HOME PAGE Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need. What is the probability of getting a sum 9 from throws of a dice?So, P(sum of 9) = 1/9.
How many ways can you get 9 with 3 dice?So in total there are 25 ways to get a sum of 9. If you want the probability, just take this over the total number of possibilities and you get 25/63=25/216. Save this answer.
What is the probability that the sum of three dice is 9 given that exactly two are the same number?Therefore, we have a total of 15 x 6 = 90 ways that exactly two of the dice will come up as the same number. So the probability is 90/216 = 15/36 = 5/12.
What is the probability of getting sum as 3 If a dice is thrown?Answer: The probability of getting the sum as 3 is 1/18. Therefore, if two dice are thrown in the air, the probability of getting sum of 3 will be 1/18.
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