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Three identicals dice are rolled. The probability that the same number will appear on each of them is. (A) 1/6 (B) 1/36 (C) 1/18 (D) 3/28?
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Three identicals dice are rolled. The probability that the same number...
Total outcomes =6^3...... favourable outcomes tht same no.comes on each of them[(111;222,333;444;555;666)]=6..... Probability=fav outcomes/total outcomes prob=6/6^3=1/36..... HOPE U GOT IT...
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Three identicals dice are rolled. The probability that the same number...
**Solution:**
To find the probability that the same number will appear on each of the three dice, we can consider each die independently.
Each die has 6 equally likely outcomes, which are the numbers 1, 2, 3, 4, 5, and 6. Since there are three dice, the total number of possible outcomes is $6 \times 6 \times 6 = 216$.
Now, let's determine the number of favorable outcomes, i.e., the number of outcomes in which the same number appears on each die.
To have the same number on each die, we can choose any number from 1 to 6, and all three dice should show that number. There are 6 possible numbers to choose from, and each number can appear on each die in 1 way. Therefore, there are a total of 6 favorable outcomes.
Thus, the probability of getting the same number on each die is given by:
$$\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$$
Substituting the values, we get:
$$\text{Probability} = \frac{6}{216} = \frac{1}{36}$$
Therefore, the correct answer is option **(B) 1/36**.
To find the probability that the same number will appear on each of the three dice, we can consider each die independently.
Each die has 6 equally likely outcomes, which are the numbers 1, 2, 3, 4, 5, and 6. Since there are three dice, the total number of possible outcomes is $6 \times 6 \times 6 = 216$.
Now, let's determine the number of favorable outcomes, i.e., the number of outcomes in which the same number appears on each die.
To have the same number on each die, we can choose any number from 1 to 6, and all three dice should show that number. There are 6 possible numbers to choose from, and each number can appear on each die in 1 way. Therefore, there are a total of 6 favorable outcomes.
Thus, the probability of getting the same number on each die is given by:
$$\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$$
Substituting the values, we get:
$$\text{Probability} = \frac{6}{216} = \frac{1}{36}$$
Therefore, the correct answer is option **(B) 1/36**.
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Three identicals dice are rolled. The probability that the same number will appear on each of them is. (A) 1/6 (B) 1/36 (C) 1/18 (D) 3/28?
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Three identicals dice are rolled. The probability that the same number will appear on each of them is. (A) 1/6 (B) 1/36 (C) 1/18 (D) 3/28? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Three identicals dice are rolled. The probability that the same number will appear on each of them is. (A) 1/6 (B) 1/36 (C) 1/18 (D) 3/28? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three identicals dice are rolled. The probability that the same number will appear on each of them is. (A) 1/6 (B) 1/36 (C) 1/18 (D) 3/28?.
Three identicals dice are rolled. The probability that the same number will appear on each of them is. (A) 1/6 (B) 1/36 (C) 1/18 (D) 3/28? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Three identicals dice are rolled. The probability that the same number will appear on each of them is. (A) 1/6 (B) 1/36 (C) 1/18 (D) 3/28? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three identicals dice are rolled. The probability that the same number will appear on each of them is. (A) 1/6 (B) 1/36 (C) 1/18 (D) 3/28?.
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