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A digit is selected at random from either of the two sets {1, 2, 3, 4, 5, 6, 7, 8, 9} and {1, 2, 3, 4, 5, 6, 7, 8, 9}. What is the chance that the sum of the digits selected is 10 ?
- a)10/18
- b)10/81
- c)1/9
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A digit is selected at random from either of the two sets {1, 2, 3, 4,...
Solution:
Let's consider all the possible ways of selecting the digits from both sets.
There are 2 ways of selecting the digits: selecting both digits from the first set or selecting one digit from each set.
Case 1: Selecting both digits from the first set
There are 9 ways of selecting the first digit and 9 ways of selecting the second digit. Therefore, there are 9 x 9 = 81 possible ways of selecting both digits from the first set.
Out of these 81 possible ways, the pairs that add up to 10 are (1,9), (2,8), (3,7), (4,6), and (5,5). So there are 5 possible pairs that add up to 10.
Therefore, the probability of selecting a pair of digits that add up to 10 from the first set is 5/81.
Case 2: Selecting one digit from each set
There are 9 ways of selecting the digit from the first set and 9 ways of selecting the digit from the second set. Therefore, there are 9 x 9 = 81 possible ways of selecting one digit from each set.
Out of these 81 possible ways, the pairs that add up to 10 are (1,9), (2,8), (3,7), (4,6), and (5,5). So there are 5 possible pairs that add up to 10.
Therefore, the probability of selecting a pair of digits that add up to 10 by selecting one digit from each set is 5/81.
Total probability of selecting a pair of digits that add up to 10 is sum of above two probabilities.
Total probability = 5/81 + 5/81 = 10/81
Hence, the correct option is (c) 1/9.
Let's consider all the possible ways of selecting the digits from both sets.
There are 2 ways of selecting the digits: selecting both digits from the first set or selecting one digit from each set.
Case 1: Selecting both digits from the first set
There are 9 ways of selecting the first digit and 9 ways of selecting the second digit. Therefore, there are 9 x 9 = 81 possible ways of selecting both digits from the first set.
Out of these 81 possible ways, the pairs that add up to 10 are (1,9), (2,8), (3,7), (4,6), and (5,5). So there are 5 possible pairs that add up to 10.
Therefore, the probability of selecting a pair of digits that add up to 10 from the first set is 5/81.
Case 2: Selecting one digit from each set
There are 9 ways of selecting the digit from the first set and 9 ways of selecting the digit from the second set. Therefore, there are 9 x 9 = 81 possible ways of selecting one digit from each set.
Out of these 81 possible ways, the pairs that add up to 10 are (1,9), (2,8), (3,7), (4,6), and (5,5). So there are 5 possible pairs that add up to 10.
Therefore, the probability of selecting a pair of digits that add up to 10 by selecting one digit from each set is 5/81.
Total probability of selecting a pair of digits that add up to 10 is sum of above two probabilities.
Total probability = 5/81 + 5/81 = 10/81
Hence, the correct option is (c) 1/9.
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A digit is selected at random from either of the two sets {1, 2, 3, 4, 5, 6, 7, 8, 9} and {1, 2, 3, 4, 5, 6, 7, 8, 9}. What is the chance that the sum of the digits selected is 10 ?a)10/18b)10/81c)1/9d)none of theseCorrect answer is option 'C'. Can you explain this answer?
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