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Two dice are thrown simultaneously. Find the probability of getting an even number as the sum.
- a)1/2
- b)1/4
- c)1/6
- d)1/8
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Two dice are thrown simultaneously. Find the probability of getting an...
Solution:
When two dice are thrown, the possible outcomes are:
1, 1
1, 2
1, 3
1, 4
1, 5
1, 6
2, 1
2, 2
2, 3
2, 4
2, 5
2, 6
3, 1
3, 2
3, 3
3, 4
3, 5
3, 6
4, 1
4, 2
4, 3
4, 4
4, 5
4, 6
5, 1
5, 2
5, 3
5, 4
5, 5
5, 6
6, 1
6, 2
6, 3
6, 4
6, 5
6, 6
There are 36 possible outcomes when two dice are thrown.
Finding the probability of getting an even number as the sum:
When two dice are thrown, the sum of the numbers on them can range from 2 to 12.
The possible sums that are even are 2, 4, 6, 8, 10, and 12.
Out of the 36 possible outcomes, there are 18 outcomes where the sum is even:
2 (1, 1)
4 (1, 3), (3, 1), (2, 2)
6 (1, 5), (5, 1), (2, 4), (4, 2), (3, 3)
8 (2, 6), (6, 2), (4, 4)
10 (4, 6), (6, 4), (5, 5)
12 (6, 6)
Therefore, the probability of getting an even number as the sum is 18/36 or 1/2.
Hence, option A is the correct answer.
When two dice are thrown, the possible outcomes are:
1, 1
1, 2
1, 3
1, 4
1, 5
1, 6
2, 1
2, 2
2, 3
2, 4
2, 5
2, 6
3, 1
3, 2
3, 3
3, 4
3, 5
3, 6
4, 1
4, 2
4, 3
4, 4
4, 5
4, 6
5, 1
5, 2
5, 3
5, 4
5, 5
5, 6
6, 1
6, 2
6, 3
6, 4
6, 5
6, 6
There are 36 possible outcomes when two dice are thrown.
Finding the probability of getting an even number as the sum:
When two dice are thrown, the sum of the numbers on them can range from 2 to 12.
The possible sums that are even are 2, 4, 6, 8, 10, and 12.
Out of the 36 possible outcomes, there are 18 outcomes where the sum is even:
2 (1, 1)
4 (1, 3), (3, 1), (2, 2)
6 (1, 5), (5, 1), (2, 4), (4, 2), (3, 3)
8 (2, 6), (6, 2), (4, 4)
10 (4, 6), (6, 4), (5, 5)
12 (6, 6)
Therefore, the probability of getting an even number as the sum is 18/36 or 1/2.
Hence, option A is the correct answer.
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Community Answer
Two dice are thrown simultaneously. Find the probability of getting an...
Solution:
When two dice are thrown, the possible outcomes are:
{(1,1), (1,2), (1,3), (1,4), (1,5), (1,6),
(2,1), (2,2), (2,3), (2,4), (2,5), (2,6),
(3,1), (3,2), (3,3), (3,4), (3,5), (3,6),
(4,1), (4,2), (4,3), (4,4), (4,5), (4,6),
(5,1), (5,2), (5,3), (5,4), (5,5), (5,6),
(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}
There are a total of 36 possible outcomes.
Getting an even sum:
To get an even sum, we need to get either two even numbers or two odd numbers.
Two even numbers:
When two even numbers are thrown, the possible outcomes are:
{(2,2), (2,4), (2,6),
(4,2), (4,4), (4,6),
(6,2), (6,4), (6,6)}
There are a total of 9 possible outcomes.
Two odd numbers:
When two odd numbers are thrown, the possible outcomes are:
{(1,3), (1,5), (3,1), (3,5), (5,1), (5,3)}
There are a total of 6 possible outcomes.
Therefore, the probability of getting an even sum is:
P(even sum) = P(two even numbers) + P(two odd numbers)
= 9/36 + 6/36
= 15/36
= 5/12
Hence, the given answer option 'A' i.e 1/2 is correct.
When two dice are thrown, the possible outcomes are:
{(1,1), (1,2), (1,3), (1,4), (1,5), (1,6),
(2,1), (2,2), (2,3), (2,4), (2,5), (2,6),
(3,1), (3,2), (3,3), (3,4), (3,5), (3,6),
(4,1), (4,2), (4,3), (4,4), (4,5), (4,6),
(5,1), (5,2), (5,3), (5,4), (5,5), (5,6),
(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}
There are a total of 36 possible outcomes.
Getting an even sum:
To get an even sum, we need to get either two even numbers or two odd numbers.
Two even numbers:
When two even numbers are thrown, the possible outcomes are:
{(2,2), (2,4), (2,6),
(4,2), (4,4), (4,6),
(6,2), (6,4), (6,6)}
There are a total of 9 possible outcomes.
Two odd numbers:
When two odd numbers are thrown, the possible outcomes are:
{(1,3), (1,5), (3,1), (3,5), (5,1), (5,3)}
There are a total of 6 possible outcomes.
Therefore, the probability of getting an even sum is:
P(even sum) = P(two even numbers) + P(two odd numbers)
= 9/36 + 6/36
= 15/36
= 5/12
Hence, the given answer option 'A' i.e 1/2 is correct.
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