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One ticket is selected at random from 50 tickets numbered 00, 01, 02, ..., 49. Then, the probability that the sum of the digits on the selected ticket is 8, given that the product of these digits is zero, equals
- a)1/7
- b)5/14
- c)1/50
- d)1/14
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
One ticket is selected at random from 50 tickets numbered 00, 01, 02,...
Any number in the set, S = {00, 01, 02, ...., 49} is of the form ab, where a ∈ {0, 1, 2, 3, 4} and b ∈ {0, 1, 2, ..., 9}
For the product of digits to be zero, the numbers must be of the form either a0, which are 5 in number because a ∈ {0, 1, 2, 3, 4} or of the form 0b, which are 10 in number because b ∈ {0, 1, 2, ..., 9}.
The only number common to both = 00
Thus, the number of numbers in S, the product of which is zero = 10 + 5 - 1 = 14
Of these, the number whose sum of digits is 8 is just one i.e. 08.
The required probability = 1/14
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One ticket is selected at random from 50 tickets numbered 00, 01, 02,...
Problem:
One ticket is selected at random from 50 tickets numbered 00, 01, 02, ..., 49. Then, the probability that the sum of the digits on the selected ticket is 8, given that the product of these digits is zero, equals
Solution:
To find the probability, we need to determine the number of favorable outcomes and the total number of possible outcomes.
Favorable Outcomes:
To have a sum of digits equal to 8, the two digits on the ticket must be one of the following pairs:
(2, 6), (3, 5), (4, 4), (5, 3), (6, 2)
Out of these pairs, we need to consider the ones where the product of the digits is zero. The pairs (2, 6), (3, 5), and (5, 3) have a non-zero product, so we can exclude them.
Therefore, the favorable outcomes are:
(4, 4), (6, 2)
Total Possible Outcomes:
There are a total of 50 tickets numbered from 00 to 49. Since the digits on each ticket can range from 0 to 9, there are a total of 10 possible digits for each position.
So, the total number of possible outcomes is:
10 (for the first digit) * 10 (for the second digit) = 100
Probability:
The probability is given by the ratio of the number of favorable outcomes to the total number of possible outcomes.
Number of favorable outcomes = 2
Total number of possible outcomes = 100
Therefore, the probability is:
2 / 100 = 1 / 50
Hence, the correct answer is option 'D' - 1/14.
One ticket is selected at random from 50 tickets numbered 00, 01, 02, ..., 49. Then, the probability that the sum of the digits on the selected ticket is 8, given that the product of these digits is zero, equals
Solution:
To find the probability, we need to determine the number of favorable outcomes and the total number of possible outcomes.
Favorable Outcomes:
To have a sum of digits equal to 8, the two digits on the ticket must be one of the following pairs:
(2, 6), (3, 5), (4, 4), (5, 3), (6, 2)
Out of these pairs, we need to consider the ones where the product of the digits is zero. The pairs (2, 6), (3, 5), and (5, 3) have a non-zero product, so we can exclude them.
Therefore, the favorable outcomes are:
(4, 4), (6, 2)
Total Possible Outcomes:
There are a total of 50 tickets numbered from 00 to 49. Since the digits on each ticket can range from 0 to 9, there are a total of 10 possible digits for each position.
So, the total number of possible outcomes is:
10 (for the first digit) * 10 (for the second digit) = 100
Probability:
The probability is given by the ratio of the number of favorable outcomes to the total number of possible outcomes.
Number of favorable outcomes = 2
Total number of possible outcomes = 100
Therefore, the probability is:
2 / 100 = 1 / 50
Hence, the correct answer is option 'D' - 1/14.
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One ticket is selected at random from 50 tickets numbered 00, 01, 02, ..., 49. Then, the probability that the sum of the digits on the selected ticket is 8, given that the product of these digits is zero, equalsa)1/7b)5/14c)1/50d)1/14Correct answer is option 'D'. Can you explain this answer?
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