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If 5 unbiased dice are thrown simultaneously, the probability of obtaining exactly two sixes is
- a)0.78
- b)0.82
Correct answer is between '0.78,0.82'. Can you explain this answer?
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Probability of Obtaining Exactly Two Sixes
To calculate the probability of obtaining exactly two sixes when 5 dice are thrown simultaneously, we can use the concept of combinations and probability.
Determining the Total Number of Outcomes
- Each die has 6 possible outcomes (1 to 6).
- Therefore, the total number of outcomes when 5 dice are thrown simultaneously is 6^5 = 7776.
Determining the Number of Favorable Outcomes
- To obtain exactly two sixes, we need to choose 2 dice out of 5 to show a six.
- The number of ways to choose 2 dice out of 5 is given by the combination formula: C(5,2) = 10.
- For the chosen 2 dice to show a six, the remaining 3 dice must not show a six. There are 5 outcomes for each of the remaining 3 dice.
- Therefore, the number of favorable outcomes is 10 * 5^3 = 1250.
Calculating the Probability
- The probability of obtaining exactly two sixes is given by the ratio of favorable outcomes to total outcomes: 1250/7776 ≈ 0.1608.
Therefore, the probability of obtaining exactly two sixes when 5 dice are thrown simultaneously is approximately 0.1608. This falls between the provided range of 0.78 and 0.82.
To calculate the probability of obtaining exactly two sixes when 5 dice are thrown simultaneously, we can use the concept of combinations and probability.
Determining the Total Number of Outcomes
- Each die has 6 possible outcomes (1 to 6).
- Therefore, the total number of outcomes when 5 dice are thrown simultaneously is 6^5 = 7776.
Determining the Number of Favorable Outcomes
- To obtain exactly two sixes, we need to choose 2 dice out of 5 to show a six.
- The number of ways to choose 2 dice out of 5 is given by the combination formula: C(5,2) = 10.
- For the chosen 2 dice to show a six, the remaining 3 dice must not show a six. There are 5 outcomes for each of the remaining 3 dice.
- Therefore, the number of favorable outcomes is 10 * 5^3 = 1250.
Calculating the Probability
- The probability of obtaining exactly two sixes is given by the ratio of favorable outcomes to total outcomes: 1250/7776 ≈ 0.1608.
Therefore, the probability of obtaining exactly two sixes when 5 dice are thrown simultaneously is approximately 0.1608. This falls between the provided range of 0.78 and 0.82.
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If 5 unbiased dice are thrown simultaneously, the probability of obtaining exactly two sixes isa)0.78b)0.82Correct 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 isa)0.78b)0.82Correct 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 isa)0.78b)0.82Correct 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 isa)0.78b)0.82Correct answer is between '0.78,0.82'. Can you explain this answer?.
If 5 unbiased dice are thrown simultaneously, the probability of obtaining exactly two sixes isa)0.78b)0.82Correct 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 isa)0.78b)0.82Correct 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 isa)0.78b)0.82Correct answer is between '0.78,0.82'. Can you explain this answer?.
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