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Two dice are thrown together. The probability of the event that the sum of nos. shown is greater than 5 is
- a)13/18
- b)15/18
- c)1
- d)none
Correct answer is option 'A'. Can you explain this answer?
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Two dice are thrown together. The probability of the event that the su...
Solution:
When two dice are thrown together, the total number of possible outcomes is 6 x 6 = 36. Let A be the event that the sum of numbers shown is greater than 5.
To find the probability of A, we need to count the number of outcomes that satisfy the condition of A. We can do this by listing all the possible outcomes and counting the ones that satisfy A. However, this method can be time-consuming, so we will use a different approach.
Let B be the event that the sum of numbers shown is less than or equal to 5. The complement of A is the event that the sum of numbers shown is less than or equal to 5, i.e., A' = B.
We can find the probability of A' by counting the number of outcomes that satisfy B. To do this, we can use a table to list all the possible outcomes and mark the ones that satisfy B.
| | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | X | | | | | |
| 2 | X | X | | | | |
| 3 | X | X | X | | | |
| 4 | X | X | X | X | | |
| 5 | X | X | X | X | X | |
| 6 | X | X | X | X | X | X |
From the table, we see that there are 15 outcomes that satisfy B. Therefore, P(B) = 15/36.
Since A' = B, we have P(A') = P(B) = 15/36.
Using the formula P(A) = 1 - P(A'), we get:
P(A) = 1 - P(B) = 1 - 15/36 = 21/36 = 7/12.
Therefore, the probability of the event that the sum of numbers shown is greater than 5 is 7/12, which is closest to option A, 13/18.
When two dice are thrown together, the total number of possible outcomes is 6 x 6 = 36. Let A be the event that the sum of numbers shown is greater than 5.
To find the probability of A, we need to count the number of outcomes that satisfy the condition of A. We can do this by listing all the possible outcomes and counting the ones that satisfy A. However, this method can be time-consuming, so we will use a different approach.
Let B be the event that the sum of numbers shown is less than or equal to 5. The complement of A is the event that the sum of numbers shown is less than or equal to 5, i.e., A' = B.
We can find the probability of A' by counting the number of outcomes that satisfy B. To do this, we can use a table to list all the possible outcomes and mark the ones that satisfy B.
| | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | X | | | | | |
| 2 | X | X | | | | |
| 3 | X | X | X | | | |
| 4 | X | X | X | X | | |
| 5 | X | X | X | X | X | |
| 6 | X | X | X | X | X | X |
From the table, we see that there are 15 outcomes that satisfy B. Therefore, P(B) = 15/36.
Since A' = B, we have P(A') = P(B) = 15/36.
Using the formula P(A) = 1 - P(A'), we get:
P(A) = 1 - P(B) = 1 - 15/36 = 21/36 = 7/12.
Therefore, the probability of the event that the sum of numbers shown is greater than 5 is 7/12, which is closest to option A, 13/18.
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Two dice are thrown together. The probability of the event that the sum of nos. shown is greater than 5 isa)13/18b)15/18c)1d)noneCorrect answer is option 'A'. Can you explain this answer?
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