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Two unbiased dice are rolled simultaneously. Find the probability of getting sum greater than 5.
- a)13/18
- b)23/36
- c)7/9
- d)5/9
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Two unbiased dice are rolled simultaneously. Find the probability of g...
Given:
Number of unbiased dice = 2
Concept:
Probability (Event) = Number of favorable outcome / Total outcome
Calculation:
No. of ways of rolling a pair of dice = 6 × 6 = 36
Let E = event of getting a sum greater than 5 = {(1, 6), (1, 5), (2, 6),(2, 5), (2, 4), (3, 6), (3, 5), (3, 4), (3, 3), (4, 6), (4, 5), (4, 4), (4, 3), (4, 2), (5, 6), (5, 5),(5, 4), (5, 3), (5, 2), (5, 1), (6, 6), (6, 5), (6, 4), (6, 3), (6, 2), (6,1)}
n(E) = 26
⇒ Required probability = 26/36 = 13/18
⇒ The probability of getting sum greater than 5 = 13/18
Alternate Method:
Alternate Method:
Given:
Number of unbiased dice = 2
Concept:
Probability (Event) = 1 - (Number of non favorable outcome / Total outcome)
Probability of getting a sum greater than 5 = 1 - (Probability of getting a sum less than or equal to 5)
Calculation:
No. of ways of rolling a pair of dice = 6 × 6 = 36
Let F = event of getting a sum less than or equal to 5 = {(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (4,1)}
n(F) = 10
⇒ Required probability = 1 - (10/36) = 1 - (5/18) = 13/18
∴ The probability of getting sum greater than 5 = 13/18
Important Points
Important Points
When we have a large number of cases like 26 in case of Event (E) then we calculate non-favorable outcome(Compliment event i.e. 1 - favourable event)
Mistake Points
In this question, we have to avoid the cases in which sum of digit is equal to five like{(1, 4),(2, 3),(3, 2),(4,1)}
Additional Information
Probabilities for the two dice
Most Upvoted Answer
Two unbiased dice are rolled simultaneously. Find the probability of g...
Understanding the Problem
When two unbiased dice are rolled, each die has 6 faces, resulting in a total of 36 possible outcomes (6 x 6). We want to find the probability of the sum of the two dice being greater than 5.
Calculating Total Outcomes
- Total outcomes when rolling two dice: 36
Finding Favorable Outcomes
To determine the sum greater than 5, we can find the total outcomes with sums less than or equal to 5 and subtract from the total outcomes.
- Possible sums and their outcomes:
- Sum = 2: (1,1) → 1 outcome
- Sum = 3: (1,2), (2,1) → 2 outcomes
- Sum = 4: (1,3), (2,2), (3,1) → 3 outcomes
- Sum = 5: (1,4), (2,3), (3,2), (4,1) → 4 outcomes
- Total outcomes for sums less than or equal to 5:
- 1 (sum 2) + 2 (sum 3) + 3 (sum 4) + 4 (sum 5) = 10 outcomes
Calculating Favorable Outcomes
- Outcomes with sums greater than 5:
- Total outcomes: 36
- Outcomes with sums less than or equal to 5: 10
- Outcomes with sums greater than 5: 36 - 10 = 26 outcomes
Calculating the Probability
- Probability of getting a sum greater than 5:
- P(sum > 5) = Favorable outcomes / Total outcomes
- P(sum > 5) = 26 / 36 = 13 / 18
Conclusion
Thus, the probability of getting a sum greater than 5 when rolling two unbiased dice is 13/18, which corresponds to option A.
When two unbiased dice are rolled, each die has 6 faces, resulting in a total of 36 possible outcomes (6 x 6). We want to find the probability of the sum of the two dice being greater than 5.
Calculating Total Outcomes
- Total outcomes when rolling two dice: 36
Finding Favorable Outcomes
To determine the sum greater than 5, we can find the total outcomes with sums less than or equal to 5 and subtract from the total outcomes.
- Possible sums and their outcomes:
- Sum = 2: (1,1) → 1 outcome
- Sum = 3: (1,2), (2,1) → 2 outcomes
- Sum = 4: (1,3), (2,2), (3,1) → 3 outcomes
- Sum = 5: (1,4), (2,3), (3,2), (4,1) → 4 outcomes
- Total outcomes for sums less than or equal to 5:
- 1 (sum 2) + 2 (sum 3) + 3 (sum 4) + 4 (sum 5) = 10 outcomes
Calculating Favorable Outcomes
- Outcomes with sums greater than 5:
- Total outcomes: 36
- Outcomes with sums less than or equal to 5: 10
- Outcomes with sums greater than 5: 36 - 10 = 26 outcomes
Calculating the Probability
- Probability of getting a sum greater than 5:
- P(sum > 5) = Favorable outcomes / Total outcomes
- P(sum > 5) = 26 / 36 = 13 / 18
Conclusion
Thus, the probability of getting a sum greater than 5 when rolling two unbiased dice is 13/18, which corresponds to option A.
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Community Answer
Two unbiased dice are rolled simultaneously. Find the probability of g...
Given:
Number of unbiased dice = 2
Concept:
Probability (Event) = Number of favorable outcome / Total outcome
Calculation:
No. of ways of rolling a pair of dice = 6 × 6 = 36
Let E = event of getting a sum greater than 5 = {(1, 6), (1, 5), (2, 6),(2, 5), (2, 4), (3, 6), (3, 5), (3, 4), (3, 3), (4, 6), (4, 5), (4, 4), (4, 3), (4, 2), (5, 6), (5, 5),(5, 4), (5, 3), (5, 2), (5, 1), (6, 6), (6, 5), (6, 4), (6, 3), (6, 2), (6,1)}
n(E) = 26
⇒ Required probability = 26/36 = 13/18
⇒ The probability of getting sum greater than 5 = 13/18
Alternate Method:
Alternate Method:
Given:
Number of unbiased dice = 2
Concept:
Probability (Event) = 1 - (Number of non favorable outcome / Total outcome)
Probability of getting a sum greater than 5 = 1 - (Probability of getting a sum less than or equal to 5)
Calculation:
No. of ways of rolling a pair of dice = 6 × 6 = 36
Let F = event of getting a sum less than or equal to 5 = {(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (4,1)}
n(F) = 10
⇒ Required probability = 1 - (10/36) = 1 - (5/18) = 13/18
∴ The probability of getting sum greater than 5 = 13/18
Important Points
Important Points
When we have a large number of cases like 26 in case of Event (E) then we calculate non-favorable outcome(Compliment event i.e. 1 - favourable event)
Mistake Points
In this question, we have to avoid the cases in which sum of digit is equal to five like{(1, 4),(2, 3),(3, 2),(4,1)}
Additional Information
Probabilities for the two dice
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Two unbiased dice are rolled simultaneously. Find the probability of getting sum greater than 5.a)13/18b)23/36c)7/9d)5/9Correct answer is option 'A'. Can you explain this answer?
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