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two dice are rolled simultaneously. find the probability of getting the sum as 3 or 4
Verified Answer
two dice are rolled simultaneously. find the probability of getting th...
Explanation:
Here n(S) = 6 x 6 = 36
E={(1,2),(1,5),(2,1),(2,4),(3,3),(3,6),(4,2),(4,5),(5,1),(5,4),(6,3) ,(6,6),(1,3),(2,2),(2,6),(3,1),(3,5), (4,4),(5,3),(6,2)}
=> n(E)=20
Required Probability n(P) = n(E)/n(S) = 20/36 = 5/9.
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Most Upvoted Answer
two dice are rolled simultaneously. find the probability of getting th...
Understanding the Problem
When two dice are rolled, the possible outcomes can be calculated by considering the total number of combinations. Each die has 6 faces, so the total outcomes when rolling two dice is:
- Total Outcomes = 6 (for the first die) × 6 (for the second die) = 36
Now, we need to find the probability of getting a sum of either 3 or 4.
Calculating Outcomes for Sum of 3
To find the combinations that give a sum of 3, we can list them:
- (1, 2)
- (2, 1)
Thus, there are 2 outcomes that result in a sum of 3.
Calculating Outcomes for Sum of 4
Next, we calculate the combinations that yield a sum of 4:
- (1, 3)
- (2, 2)
- (3, 1)
Here, we have 3 outcomes that result in a sum of 4.
Total Favorable Outcomes
Now, we combine the outcomes for both sums:
- Total Favorable Outcomes = Outcomes for Sum of 3 + Outcomes for Sum of 4
- Total Favorable Outcomes = 2 + 3 = 5
Calculating the Probability
The probability of an event is calculated using the formula:
- Probability = (Number of Favorable Outcomes) / (Total Outcomes)
So, in this case:
- Probability = 5 / 36
Final Answer
Therefore, the probability of getting a sum of either 3 or 4 when rolling two dice is:
- 5/36
When two dice are rolled, the possible outcomes can be calculated by considering the total number of combinations. Each die has 6 faces, so the total outcomes when rolling two dice is:
- Total Outcomes = 6 (for the first die) × 6 (for the second die) = 36
Now, we need to find the probability of getting a sum of either 3 or 4.
Calculating Outcomes for Sum of 3
To find the combinations that give a sum of 3, we can list them:
- (1, 2)
- (2, 1)
Thus, there are 2 outcomes that result in a sum of 3.
Calculating Outcomes for Sum of 4
Next, we calculate the combinations that yield a sum of 4:
- (1, 3)
- (2, 2)
- (3, 1)
Here, we have 3 outcomes that result in a sum of 4.
Total Favorable Outcomes
Now, we combine the outcomes for both sums:
- Total Favorable Outcomes = Outcomes for Sum of 3 + Outcomes for Sum of 4
- Total Favorable Outcomes = 2 + 3 = 5
Calculating the Probability
The probability of an event is calculated using the formula:
- Probability = (Number of Favorable Outcomes) / (Total Outcomes)
So, in this case:
- Probability = 5 / 36
Final Answer
Therefore, the probability of getting a sum of either 3 or 4 when rolling two dice is:
- 5/36
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two dice are rolled simultaneously. find the probability of getting the sum as 3 or 4 Related: Equal Likely Outcomes:Throwing a Die, Data Handling, Class 8 Math
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