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01 Jan 2024, 06:13
Kudos
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D
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Difficulty:
35%
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Question Stats:
69% (01:04) correct
31%
(01:13)
wrong
based on 662
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A number is selected at random from a list of the first 10 positive integers. What is the probability that the number selected will be odd or divisible by 3?
A. \(\frac{3}{20}\)
B. \(\frac{1}{2}\)
C. \(\frac{13}{20}\)
D. \(\frac{3}{5}\)
E. \(\frac{4}{5}\)
Screenshot 2024-01-01 183950.png [ 74.26 KiB | Viewed 9550 times ]
A. \(\frac{3}{20}\)
B. \(\frac{1}{2}\)
C. \(\frac{13}{20}\)
D. \(\frac{3}{5}\)
E. \(\frac{4}{5}\)
Attachment:
Screenshot 2024-01-01 183950.png [ 74.26 KiB | Viewed 9550 times ]
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01 Jan 2024, 06:38
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To find the probability that the number selected will be odd or divisible by 3, we first need to determine the count of numbers that satisfy either condition and then divide it by the total number of possible outcomes.
The first 10 positive integers are: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
Odd numbers: 1, 3, 5, 7, 9 (5 numbers)
Numbers divisible by 3: 3, 6, 9 (3 numbers)
Now, we need to find the numbers that satisfy either condition without double-counting. The numbers that are both odd and divisible by 3 are 3 and 9.
So, the total count of numbers that are either odd or divisible by 3 is: 5 (odd) + 3 (divisible by 3) - 2 (both) = 6.
The total number of possible outcomes is 10.
Now, we can calculate the probability:
Probability= Number of Favorable Outcomes / Total Number of Possible Outcomes
Probability = 6/10 = 0.6 =3/5
Therefore, the probability that the number selected will be odd or divisible by 3 is 3/5
The first 10 positive integers are: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
Odd numbers: 1, 3, 5, 7, 9 (5 numbers)
Numbers divisible by 3: 3, 6, 9 (3 numbers)
Now, we need to find the numbers that satisfy either condition without double-counting. The numbers that are both odd and divisible by 3 are 3 and 9.
So, the total count of numbers that are either odd or divisible by 3 is: 5 (odd) + 3 (divisible by 3) - 2 (both) = 6.
The total number of possible outcomes is 10.
Now, we can calculate the probability:
Probability= Number of Favorable Outcomes / Total Number of Possible Outcomes
Probability = 6/10 = 0.6 =3/5
Therefore, the probability that the number selected will be odd or divisible by 3 is 3/5
01 Jan 2024, 06:41
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Souvik7
Note that there is an overlap between odd numbers and multiples of 3. Specifically, 3 and 9 are both odd and multiples of 3, so the probability of this overlap should be subtracted from your result. This leads to 4/5 - 2/10 = 3/5.
Answer: D.
