GATE EC 2017 Set 1 — Question 4
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Engineering Mathematics → Probability → Combinatorial Probability
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Question
Three fair cubical dice are thrown simultaneously. The probability that all three dice have the same number of dots on the faces showing up is (up to third decimal place) __________
Correct answer
0.027 to 0.028
Solution
When three fair cubical dice are thrown simultaneously, the total number of possible outcomes is .The favorable outcomes, where all three dice have the same number of dots, are:
(1, 1, 1)
(2, 2, 2)
(3, 3, 3)
(4, 4, 4)
(5, 5, 5)
(6, 6, 6)
There are 6 such favorable outcomes.The probability is the ratio of favorable outcomes to the total number of outcomes:
To express this probability up to the third decimal place:
Rounding to the third decimal place, we get .Thus, the probability is .
(1, 1, 1)
(2, 2, 2)
(3, 3, 3)
(4, 4, 4)
(5, 5, 5)
(6, 6, 6)
There are 6 such favorable outcomes.The probability is the ratio of favorable outcomes to the total number of outcomes:
To express this probability up to the third decimal place:
Rounding to the third decimal place, we get .Thus, the probability is .
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