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Four normal dice are rolled once. The number of possible outcomes in which at least one die shows up 2 is -
- a)216
- b)648
- c)625
- d)671
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Four normal dice are rolled once. The number of possible outcomes in w...
Total number of outcomes when four normal dice are rolled
= 6 × 6 × 6 × 6 = 64 = 1296
Total number of ways in which no dice shows up 2 i.e.
Each of the four dice shows up 1,3,4,5 or 6 as outcomes
=5 × 5 × 5 × 5 = 54 = 625
Hence total number of possible outcomes when no dice shows up 2
=1296 − 625 = 671
= 6 × 6 × 6 × 6 = 64 = 1296
Total number of ways in which no dice shows up 2 i.e.
Each of the four dice shows up 1,3,4,5 or 6 as outcomes
=5 × 5 × 5 × 5 = 54 = 625
Hence total number of possible outcomes when no dice shows up 2
=1296 − 625 = 671
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Four normal dice are rolled once. The number of possible outcomes in w...
Calculating the number of outcomes with at least one die showing up 2
To calculate the number of outcomes in which at least one die shows up 2, we can use the concept of complementary probability. We will first calculate the total number of outcomes when four dice are rolled, and then subtract the number of outcomes in which no die shows up 2.
Total number of outcomes when four dice are rolled
When four dice are rolled, each die can show any number from 1 to 6. Therefore, the total number of outcomes is 6^4 = 1296.
Calculating the number of outcomes with no die showing up 2
When no die shows up 2, each die can show any number from 1, 3, 4, 5, or 6. Therefore, the total number of outcomes when no die shows up 2 is 5^4 = 625.
Calculating the number of outcomes with at least one die showing up 2
Now, we can subtract the number of outcomes with no die showing up 2 from the total number of outcomes to get the number of outcomes with at least one die showing up 2:
1296 - 625 = 671.
Therefore, the number of possible outcomes in which at least one die shows up 2 is 671, which matches option 'D'.
To calculate the number of outcomes in which at least one die shows up 2, we can use the concept of complementary probability. We will first calculate the total number of outcomes when four dice are rolled, and then subtract the number of outcomes in which no die shows up 2.
Total number of outcomes when four dice are rolled
When four dice are rolled, each die can show any number from 1 to 6. Therefore, the total number of outcomes is 6^4 = 1296.
Calculating the number of outcomes with no die showing up 2
When no die shows up 2, each die can show any number from 1, 3, 4, 5, or 6. Therefore, the total number of outcomes when no die shows up 2 is 5^4 = 625.
Calculating the number of outcomes with at least one die showing up 2
Now, we can subtract the number of outcomes with no die showing up 2 from the total number of outcomes to get the number of outcomes with at least one die showing up 2:
1296 - 625 = 671.
Therefore, the number of possible outcomes in which at least one die shows up 2 is 671, which matches option 'D'.
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Four normal dice are rolled once. The number of possible outcomes in which at least one die shows up 2 is -a)216b)648c)625d)671Correct answer is option 'D'. Can you explain this answer?
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Four normal dice are rolled once. The number of possible outcomes in which at least one die shows up 2 is -a)216b)648c)625d)671Correct answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Four normal dice are rolled once. The number of possible outcomes in which at least one die shows up 2 is -a)216b)648c)625d)671Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Four normal dice are rolled once. The number of possible outcomes in which at least one die shows up 2 is -a)216b)648c)625d)671Correct answer is option 'D'. Can you explain this answer?.
Four normal dice are rolled once. The number of possible outcomes in which at least one die shows up 2 is -a)216b)648c)625d)671Correct answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Four normal dice are rolled once. The number of possible outcomes in which at least one die shows up 2 is -a)216b)648c)625d)671Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Four normal dice are rolled once. The number of possible outcomes in which at least one die shows up 2 is -a)216b)648c)625d)671Correct answer is option 'D'. Can you explain this answer?.
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