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03 Apr 2019, 20:44
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
73% (01:08) correct
27%
(01:08)
wrong
based on 274
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The probability that a randomly chosen integer will end in 0 is \(\frac{1}{10}\). If two integers are chosen at random, what is the probability that at least one of them will end in 0?
A. \(\frac{1}{2}\)
B. \(\frac{1}{10}\)
C. \(\frac{1}{100}\)
D. \(\frac{19}{100}\)
E. \(\frac{81}{100}\)
A. \(\frac{1}{2}\)
B. \(\frac{1}{10}\)
C. \(\frac{1}{100}\)
D. \(\frac{19}{100}\)
E. \(\frac{81}{100}\)
03 Apr 2019, 22:11
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Solution
Given:
In this question, we are given that
- • The probability that a randomly chosen integer will end in 0 is \(\frac{1}{10}\).
• Two integers are chosen at random.
To find:
We need to determine
- • The probability that from the two randomly chosen integers, at least one of them will end in 0.
Approach and Working:
As the probability that a randomly chosen integer will end in 0 is \(\frac{1}{10}\),
- • The probability that the integer will not end in 0 = \(1 – \frac{1}{10} = \frac{9}{10}\)
Now, we can say that
P(at least one of two integers will end in 0) = 1 – P(none of the two chosen integers will end in 0)
- • P(none of the two chosen integers will end in 0) = \(\frac{9}{10} * \frac{9}{10} = \frac{81}{100}\)
• Therefore, P(at least one of the two integers will end in 0) = \(1 – \frac{81}{100} = \frac{19}{100}\)
Hence, the correct answer is option D.
Answer: D
General Discussion
eswarchethu135
03 Apr 2019, 22:39
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Probability of the last digit being 0 = \(\frac{1}{10}\)
Probability of the last digit not being 0 = \(\frac{9}{10}\)
Probability when two integers are chosen at random atleast 1 of them is 0 = 1 - P(No integer is 0)
= \(1 - (\frac{9}{10}) * (\frac{9}{10})\)
= \(1 - (\frac{81}{100})\)
= \((\frac{19}{100})\)
OPTION: D
Probability of the last digit not being 0 = \(\frac{9}{10}\)
Probability when two integers are chosen at random atleast 1 of them is 0 = 1 - P(No integer is 0)
= \(1 - (\frac{9}{10}) * (\frac{9}{10})\)
= \(1 - (\frac{81}{100})\)
= \((\frac{19}{100})\)
OPTION: D
