Probability for rolling three dice with the six sided dots such as 1, 2, 3, 4, 5 and 6 dots in each (three) dies. When three dice are thrown simultaneously/randomly, thus number of event can be 63 = (6 × 6 × 6) = 216 because each die has 1 to 6 number on its faces.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 = 1/36 (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 = 5/108 (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 = 1/54 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 = 5/108 (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 = 5/54 (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 = 5/108 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
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If three dices are thrown simultaneously, then all the possible outcomes = 63 = 216 Number of favourable outcomes, n(A) = 4 Hence, required probability, P(A) = P (sum of the numbers on three dices as 17 or 18) = \[\frac{4}{216} = \frac{1}{54}\] No worries! We‘ve got your back. Try BYJU‘S free classes today! No worries! We‘ve got your back. Try BYJU‘S free classes today! Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses No worries! We‘ve got your back. Try BYJU‘S free classes today! |