A red, a blue and a green dice are thrown at the same time, display all the possibile outcomes in a suitable way, find the probability of obtaining :
a) a total of 18 on a three dice
b) a total of 4 on a three dice
C) a total of 10
D) total of 15
E) total of 7
F) the same number on each dice
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Answers
Answer:
Hello mate..
Step-by-step explanation:
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Probability for Rolling Three Dice
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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 outcomes
P(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 outcomes
P(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 outcomes
P(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
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Step-by-step explanation:
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