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Four dice are rolled. The number of possible outcomes in which at least one dice show 2 is
- a)1296
- b)671
- c)625
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Four dice are rolled. The number of possible outcomes in which at leas...
Concept:
Permutations with Repetition = nr
Where n is the number of things to choose from r different things when repetition is allowed, and order matters.
Favorable cases = Total cases - Unfavorable cases
Calculation:
According to the question
Four dies are rolled
So, Total Possible number of outcomes = 64
Now, Total outcomes when no 2 appears = 54
Now, From the concept used
Favorable cases = 64 - 54
⇒ 1296 - 625
⇒ 671
∴ The number of possible outcomes in which at least one die shows 2 is 671.
Most Upvoted Answer
Four dice are rolled. The number of possible outcomes in which at leas...
Concept:
Permutations with Repetition = nr
Where n is the number of things to choose from r different things when repetition is allowed, and order matters.
Favorable cases = Total cases - Unfavorable cases
Calculation:
According to the question
Four dies are rolled
So, Total Possible number of outcomes = 64
Now, Total outcomes when no 2 appears = 54
Now, From the concept used
Favorable cases = 64 - 54
⇒ 1296 - 625
⇒ 671
∴ The number of possible outcomes in which at least one die shows 2 is 671.
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Community Answer
Four dice are rolled. The number of possible outcomes in which at leas...
To find the number of possible outcomes in which at least one die shows a 2, we can use the principle of complementary counting.
Principle of Complementary Counting:
Instead of directly counting the desired outcomes, we can count the total number of outcomes and subtract the number of outcomes that do not meet the desired condition.
Total Number of Outcomes:
When four dice are rolled, each die has 6 possible outcomes (numbers 1-6). Therefore, the total number of outcomes is 6^4 = 1296.
Number of Outcomes with No 2:
To find the number of outcomes in which no die shows a 2, we can consider each die independently. For each die, there are 5 possible outcomes (numbers 1, 3, 4, 5, and 6) that are not 2. Since there are 4 dice, the total number of outcomes with no 2 is 5^4 = 625.
Number of Outcomes with at Least One 2:
Now, we can use the principle of complementary counting to find the number of outcomes with at least one 2.
Number of outcomes with at least one 2 = Total number of outcomes - Number of outcomes with no 2
= 1296 - 625
= 671
Therefore, the correct answer is option B) 671.
Principle of Complementary Counting:
Instead of directly counting the desired outcomes, we can count the total number of outcomes and subtract the number of outcomes that do not meet the desired condition.
Total Number of Outcomes:
When four dice are rolled, each die has 6 possible outcomes (numbers 1-6). Therefore, the total number of outcomes is 6^4 = 1296.
Number of Outcomes with No 2:
To find the number of outcomes in which no die shows a 2, we can consider each die independently. For each die, there are 5 possible outcomes (numbers 1, 3, 4, 5, and 6) that are not 2. Since there are 4 dice, the total number of outcomes with no 2 is 5^4 = 625.
Number of Outcomes with at Least One 2:
Now, we can use the principle of complementary counting to find the number of outcomes with at least one 2.
Number of outcomes with at least one 2 = Total number of outcomes - Number of outcomes with no 2
= 1296 - 625
= 671
Therefore, the correct answer is option B) 671.
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