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A fair die is thrown three times and the sum of three numbers is found to be 16. Find the probability that 5 appears on the third throw.
- a)1/2
- b)1/3
- c)1/4
- d)1/5
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A fair die is thrown three times and the sum of three numbers is foun...
For sum = 16, we have the following cases:
(i) 6, 6, 4
(ii) 6, 4, 6
(iii) 4, 6, 6
(iv) 5, 5, 6
(v) 5, 6, 5
(vi) 6, 5, 5
Total cases of sum (16) = 6
Favourable cases for 5 appears in 3rd throw = 2
p = 2 / 6 = 1 / 3
Most Upvoted Answer
A fair die is thrown three times and the sum of three numbers is foun...
To find the probability that 5 appears on the third throw, we need to consider the possible outcomes of the three throws that result in a sum of 16.
Step 1: Find the possible outcomes
When a fair die is thrown, there are 6 possible outcomes: 1, 2, 3, 4, 5, or 6. We need to find all the possible combinations of three numbers that sum up to 16.
Let's list out all the possibilities:
1 + 1 + 14 = 16
1 + 2 + 13 = 16
1 + 3 + 12 = 16
1 + 4 + 11 = 16
1 + 5 + 10 = 16
1 + 6 + 9 = 16
2 + 1 + 13 = 16
2 + 2 + 12 = 16
2 + 3 + 11 = 16
2 + 4 + 10 = 16
2 + 5 + 9 = 16
2 + 6 + 8 = 16
3 + 1 + 12 = 16
3 + 2 + 11 = 16
3 + 3 + 10 = 16
3 + 4 + 9 = 16
3 + 5 + 8 = 16
3 + 6 + 7 = 16
4 + 1 + 11 = 16
4 + 2 + 10 = 16
4 + 3 + 9 = 16
4 + 4 + 8 = 16
4 + 5 + 7 = 16
4 + 6 + 6 = 16
5 + 1 + 10 = 16
5 + 2 + 9 = 16
5 + 3 + 8 = 16
5 + 4 + 7 = 16
5 + 5 + 6 = 16
6 + 1 + 9 = 16
6 + 2 + 8 = 16
6 + 3 + 7 = 16
6 + 4 + 6 = 16
There are a total of 31 possible outcomes.
Step 2: Find the outcomes where 5 appears on the third throw
Out of the 31 possible outcomes, we need to find the ones where 5 appears on the third throw. From the list above, we can see that there are 8 outcomes where 5 appears on the third throw.
Step 3: Calculate the probability
The probability of an event occurring is given by the ratio of favorable outcomes to total outcomes.
In this case, the probability of getting a sum of 16 and having 5 appear on the third throw is 8/31.
Therefore, the correct answer is option 'B' - 1/3.
Step 1: Find the possible outcomes
When a fair die is thrown, there are 6 possible outcomes: 1, 2, 3, 4, 5, or 6. We need to find all the possible combinations of three numbers that sum up to 16.
Let's list out all the possibilities:
1 + 1 + 14 = 16
1 + 2 + 13 = 16
1 + 3 + 12 = 16
1 + 4 + 11 = 16
1 + 5 + 10 = 16
1 + 6 + 9 = 16
2 + 1 + 13 = 16
2 + 2 + 12 = 16
2 + 3 + 11 = 16
2 + 4 + 10 = 16
2 + 5 + 9 = 16
2 + 6 + 8 = 16
3 + 1 + 12 = 16
3 + 2 + 11 = 16
3 + 3 + 10 = 16
3 + 4 + 9 = 16
3 + 5 + 8 = 16
3 + 6 + 7 = 16
4 + 1 + 11 = 16
4 + 2 + 10 = 16
4 + 3 + 9 = 16
4 + 4 + 8 = 16
4 + 5 + 7 = 16
4 + 6 + 6 = 16
5 + 1 + 10 = 16
5 + 2 + 9 = 16
5 + 3 + 8 = 16
5 + 4 + 7 = 16
5 + 5 + 6 = 16
6 + 1 + 9 = 16
6 + 2 + 8 = 16
6 + 3 + 7 = 16
6 + 4 + 6 = 16
There are a total of 31 possible outcomes.
Step 2: Find the outcomes where 5 appears on the third throw
Out of the 31 possible outcomes, we need to find the ones where 5 appears on the third throw. From the list above, we can see that there are 8 outcomes where 5 appears on the third throw.
Step 3: Calculate the probability
The probability of an event occurring is given by the ratio of favorable outcomes to total outcomes.
In this case, the probability of getting a sum of 16 and having 5 appear on the third throw is 8/31.
Therefore, the correct answer is option 'B' - 1/3.
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