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If two dice are thrown, what is the probability that the number appeared on second dice is greater than that on the first dice?
- a)5/9
- b)5/12
- c)1/2
- d)11/36
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
If two dice are thrown, what is the probability that the number appea...
Probability of one die roll:
- When a single die is rolled, there are 6 possible outcomes, as the die has 6 sides numbered from 1 to 6.
- Each outcome has an equal chance of occurring, so the probability of any specific outcome is 1/6.
Probability of the second die being greater than the first die:
- To find the probability that the number on the second die is greater than the first die, we need to consider all possible outcomes and count the favorable outcomes.
- Let's analyze the possible outcomes by listing the numbers that can appear on the first die and the corresponding numbers that can appear on the second die:
- If the number on the first die is 1, the second die can have numbers 2, 3, 4, 5, or 6. So there are 5 favorable outcomes.
- If the number on the first die is 2, the second die can have numbers 3, 4, 5, or 6. So there are 4 favorable outcomes.
- If the number on the first die is 3, the second die can have numbers 4, 5, or 6. So there are 3 favorable outcomes.
- If the number on the first die is 4, the second die can have numbers 5 or 6. So there are 2 favorable outcomes.
- If the number on the first die is 5, the second die can only have the number 6. So there is 1 favorable outcome.
- If the number on the first die is 6, there are no favorable outcomes as the second die cannot have a number greater than 6.
- In total, there are 5 + 4 + 3 + 2 + 1 = 15 favorable outcomes.
Total number of possible outcomes:
- The total number of possible outcomes when two dice are rolled is the product of the number of outcomes for each die, which is 6 x 6 = 36.
Calculating the probability:
- The probability of an event happening is given by the ratio of the number of favorable outcomes to the total number of possible outcomes.
- In this case, the probability of the number on the second die being greater than the first die is 15/36.
- This can be simplified to 5/12, which is the correct answer (option B).
- When a single die is rolled, there are 6 possible outcomes, as the die has 6 sides numbered from 1 to 6.
- Each outcome has an equal chance of occurring, so the probability of any specific outcome is 1/6.
Probability of the second die being greater than the first die:
- To find the probability that the number on the second die is greater than the first die, we need to consider all possible outcomes and count the favorable outcomes.
- Let's analyze the possible outcomes by listing the numbers that can appear on the first die and the corresponding numbers that can appear on the second die:
- If the number on the first die is 1, the second die can have numbers 2, 3, 4, 5, or 6. So there are 5 favorable outcomes.
- If the number on the first die is 2, the second die can have numbers 3, 4, 5, or 6. So there are 4 favorable outcomes.
- If the number on the first die is 3, the second die can have numbers 4, 5, or 6. So there are 3 favorable outcomes.
- If the number on the first die is 4, the second die can have numbers 5 or 6. So there are 2 favorable outcomes.
- If the number on the first die is 5, the second die can only have the number 6. So there is 1 favorable outcome.
- If the number on the first die is 6, there are no favorable outcomes as the second die cannot have a number greater than 6.
- In total, there are 5 + 4 + 3 + 2 + 1 = 15 favorable outcomes.
Total number of possible outcomes:
- The total number of possible outcomes when two dice are rolled is the product of the number of outcomes for each die, which is 6 x 6 = 36.
Calculating the probability:
- The probability of an event happening is given by the ratio of the number of favorable outcomes to the total number of possible outcomes.
- In this case, the probability of the number on the second die being greater than the first die is 15/36.
- This can be simplified to 5/12, which is the correct answer (option B).
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Community Answer
If two dice are thrown, what is the probability that the number appea...
Total number of events = 36
If first dice gives 1, the second dice can be any number from 2 to 6.
Similarly, the favorable events are (1, 2) … (1, 6), (2, 3)...(2, 6), (3, 4), (3, 5), (3, 6), (4, 5), (4, 6), (5, 6).
So total number of favorable events = 15
Required Probability = 15/36 = 5/12
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