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23 Apr 2024, 11:10
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A
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76% (02:27) correct
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A lottery box contains 8,000 tickets, each of which is red or blue or green. The box contains twice as many blue tickets as red tickets. The number of green tickets is 20 more than the number of red and blue tickets combined. Which of the following is the best approximation to the probability that the first ticket randomly drawn from the box will be blue?
A. 1/3
B. 1/4
C. 1/5
D. 1/6
E. 1/8
A. 1/3
B. 1/4
C. 1/5
D. 1/6
E. 1/8
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23 Apr 2024, 11:18
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A lottery box contains 8,000 tickets, each of which is red or blue or green. The box contains twice as many blue tickets as red tickets. The number of green tickets is 20 more than the number of red and blue tickets combined. Which of the following is the best approximation to the probability that the first ticket randomly drawn from the box will be blue?
To determine the probability that the first ticket drawn will be blue, we need to find the proportion of the tickets that are blue.
Let B be the number of blue tickets.
We have the following information:
The box contains twice as many blue tickets as red tickets.
So, we know that blue + red = B + B/2.
The number of green tickets is 20 more than the number of red and blue tickets combined.
Since 20 out of 8,000 is a negligible number, we can also say the following:
green ≈ B + B/2
So, blue + red + green ≈ 2(B + B/2) ≈ 3B
So, B = Total/3.
Thus, the probability of choosing a blue ticket is about 1/3.
A. 1/3
B. 1/4
C. 1/5
D. 1/6
E. 1/8
Correct answer: A
To determine the probability that the first ticket drawn will be blue, we need to find the proportion of the tickets that are blue.
Let B be the number of blue tickets.
We have the following information:
The box contains twice as many blue tickets as red tickets.
So, we know that blue + red = B + B/2.
The number of green tickets is 20 more than the number of red and blue tickets combined.
Since 20 out of 8,000 is a negligible number, we can also say the following:
green ≈ B + B/2
So, blue + red + green ≈ 2(B + B/2) ≈ 3B
So, B = Total/3.
Thus, the probability of choosing a blue ticket is about 1/3.
A. 1/3
B. 1/4
C. 1/5
D. 1/6
E. 1/8
Correct answer: A
23 Apr 2024, 11:19
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Bunuel
- A lottery box contains 8,000 tickets, each of which is red or blue or green: b + g + r = 8000
- The box contains twice as many blue tickets as red tickets b = 2r
- The number of green tickets is 20 more than the number of red and blue tickets combined: g - 20 = b + r
The question ask to find the approximate value of b/8,000.
- Substituting g - 20 = b + r into b + g + r = 8000 we get g + (g - 20) = 8000, which gives g = 4,010.
- Substituting g = 4,010 into g - 20 = b + r we get 4,010 - 20 = b + r, which gives r = 3,990 - b.
- Substituting r = 3,990 - b into b = 2r we get b = 2(3,990 - b), which gives b = 2,660.
Therefore, b/8,000 = 2,660/8,000 = 133/400 ≈ 1/3.
Answer: A.
