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3 fair and unbiased dice are rolled at a time the probability that numbers are totally different?
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3 fair and unbiased dice are rolled at a time the probability that num...
Calculating the probability of rolling 3 different numbers on 3 dice:
To calculate the probability of rolling 3 different numbers on 3 dice, we need to first determine the total number of possible outcomes when rolling 3 dice.
Determining the total number of possible outcomes:
When rolling 3 dice, each die can land on one of 6 possible numbers. Therefore, the total number of possible outcomes is:
6 x 6 x 6 = 216
Determining the number of outcomes where all 3 numbers are different:
To determine the number of outcomes where all 3 numbers are different, we can use the following formula:
n! / (n-r)!
Where n is the total number of possible outcomes (216) and r is the number of dice being rolled (3).
Using this formula, we get:
6! / (6-3)! = 6 x 5 x 4 = 120
Therefore, there are 120 possible outcomes where all 3 numbers are different.
Calculating the probability:
To calculate the probability of rolling 3 different numbers on 3 dice, we simply divide the number of outcomes where all 3 numbers are different by the total number of possible outcomes:
120 / 216 = 5/9
Therefore, the probability of rolling 3 different numbers on 3 dice is approximately 0.556 or 55.6%.
To calculate the probability of rolling 3 different numbers on 3 dice, we need to first determine the total number of possible outcomes when rolling 3 dice.
Determining the total number of possible outcomes:
When rolling 3 dice, each die can land on one of 6 possible numbers. Therefore, the total number of possible outcomes is:
6 x 6 x 6 = 216
Determining the number of outcomes where all 3 numbers are different:
To determine the number of outcomes where all 3 numbers are different, we can use the following formula:
n! / (n-r)!
Where n is the total number of possible outcomes (216) and r is the number of dice being rolled (3).
Using this formula, we get:
6! / (6-3)! = 6 x 5 x 4 = 120
Therefore, there are 120 possible outcomes where all 3 numbers are different.
Calculating the probability:
To calculate the probability of rolling 3 different numbers on 3 dice, we simply divide the number of outcomes where all 3 numbers are different by the total number of possible outcomes:
120 / 216 = 5/9
Therefore, the probability of rolling 3 different numbers on 3 dice is approximately 0.556 or 55.6%.
Community Answer
3 fair and unbiased dice are rolled at a time the probability that num...
total no. of outcomes=6^3=216
no. of similar no. = 36+30+30=96
result outcome =216-96=120
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3 fair and unbiased dice are rolled at a time the probability that numbers are totally different?
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3 fair and unbiased dice are rolled at a time the probability that numbers are totally different? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about 3 fair and unbiased dice are rolled at a time the probability that numbers are totally different? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 3 fair and unbiased dice are rolled at a time the probability that numbers are totally different?.
3 fair and unbiased dice are rolled at a time the probability that numbers are totally different? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about 3 fair and unbiased dice are rolled at a time the probability that numbers are totally different? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 3 fair and unbiased dice are rolled at a time the probability that numbers are totally different?.
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