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If 5 unbiased dice are thrown simultaneously, the probability of obtaining exactly two sixes is
Correct answer is between '0.78,0.82'. Can you explain this answer?
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Calculating the Probability of Obtaining Exactly Two Sixes with 5 Dice
To calculate the probability of obtaining exactly two sixes when throwing five unbiased dice simultaneously, we need to consider the number of favorable outcomes and the total number of possible outcomes.
Step 1: Calculating the Total Number of Possible Outcomes
When throwing a single unbiased die, there are six possible outcomes: 1, 2, 3, 4, 5, and 6. Since we are throwing five dice simultaneously, the total number of possible outcomes can be calculated using the multiplication principle.
Total number of possible outcomes = 6^5 = 7776
Step 2: Calculating the Number of Favorable Outcomes
To calculate the number of favorable outcomes, we need to consider all the possible combinations of obtaining exactly two sixes with five dice. We can do this by using the concept of combinations.
The number of ways to choose two positions for the sixes out of the five dice is given by the combination formula:
Number of favorable outcomes = C(5, 2) = 5! / (2! * (5-2)!) = 10
For each of these combinations, the remaining three dice can have any of the remaining five numbers (1, 2, 3, 4, or 5) on their faces. Therefore, the number of ways to assign these numbers to the remaining three dice is given by:
Number of ways to assign numbers to the remaining three dice = 5^3 = 125
Hence, the total number of favorable outcomes can be calculated as:
Number of favorable outcomes = Number of combinations * Number of ways to assign numbers
= 10 * 125
= 1250
Step 3: Calculating the Probability
Now that we have the number of favorable outcomes and the total number of possible outcomes, we can calculate the probability.
Probability = Number of favorable outcomes / Total number of possible outcomes
= 1250 / 7776
≈ 0.1607
Step 4: Interpreting the Probability Range
The given correct answer range is '0.78, 0.82', which means the probability lies between 0.78 and 0.82. However, the calculated probability of approximately 0.1607 does not fall within this range.
It is possible that there may be a mistake in the given answer range or in the calculation. Double-checking the calculations or verifying the answer range may be necessary to ensure accuracy.
Overall, the probability of obtaining exactly two sixes when throwing five unbiased dice simultaneously is approximately 0.1607, which does not match the given answer range.
To calculate the probability of obtaining exactly two sixes when throwing five unbiased dice simultaneously, we need to consider the number of favorable outcomes and the total number of possible outcomes.
Step 1: Calculating the Total Number of Possible Outcomes
When throwing a single unbiased die, there are six possible outcomes: 1, 2, 3, 4, 5, and 6. Since we are throwing five dice simultaneously, the total number of possible outcomes can be calculated using the multiplication principle.
Total number of possible outcomes = 6^5 = 7776
Step 2: Calculating the Number of Favorable Outcomes
To calculate the number of favorable outcomes, we need to consider all the possible combinations of obtaining exactly two sixes with five dice. We can do this by using the concept of combinations.
The number of ways to choose two positions for the sixes out of the five dice is given by the combination formula:
Number of favorable outcomes = C(5, 2) = 5! / (2! * (5-2)!) = 10
For each of these combinations, the remaining three dice can have any of the remaining five numbers (1, 2, 3, 4, or 5) on their faces. Therefore, the number of ways to assign these numbers to the remaining three dice is given by:
Number of ways to assign numbers to the remaining three dice = 5^3 = 125
Hence, the total number of favorable outcomes can be calculated as:
Number of favorable outcomes = Number of combinations * Number of ways to assign numbers
= 10 * 125
= 1250
Step 3: Calculating the Probability
Now that we have the number of favorable outcomes and the total number of possible outcomes, we can calculate the probability.
Probability = Number of favorable outcomes / Total number of possible outcomes
= 1250 / 7776
≈ 0.1607
Step 4: Interpreting the Probability Range
The given correct answer range is '0.78, 0.82', which means the probability lies between 0.78 and 0.82. However, the calculated probability of approximately 0.1607 does not fall within this range.
It is possible that there may be a mistake in the given answer range or in the calculation. Double-checking the calculations or verifying the answer range may be necessary to ensure accuracy.
Overall, the probability of obtaining exactly two sixes when throwing five unbiased dice simultaneously is approximately 0.1607, which does not match the given answer range.
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If 5 unbiased dice are thrown simultaneously, the probability of obtaining exactly two sixes isCorrect answer is between '0.78,0.82'. Can you explain this answer?
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If 5 unbiased dice are thrown simultaneously, the probability of obtaining exactly two sixes isCorrect answer is between '0.78,0.82'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about If 5 unbiased dice are thrown simultaneously, the probability of obtaining exactly two sixes isCorrect answer is between '0.78,0.82'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 5 unbiased dice are thrown simultaneously, the probability of obtaining exactly two sixes isCorrect answer is between '0.78,0.82'. Can you explain this answer?.
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