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03 Aug 2023, 03:00
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Difficulty:
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Question Stats:
66% (02:49) correct
34%
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wrong
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A box contains exactly 7 fuses, 3 of which are defective and 4 of which are not defective. In the bar graph above, the left and middle bars are the same height and the right bar is half this height. The heights are intended to represent, respectively, the probabilities of obtaining 0 defective fuses, exactly 1 defective fuse, and 2 defective fuses when 2 fuses are randomly selected without replacement from the box. However, 1 of the bar heights is incorrect. The correct height is k times the height shown. Which of the following choices for the bar and the value of k would result in an accurate representation of the labeled probabilities?
A. Middle bar; k = 1/2
B. Middle bar; k = 2
C. Left bar; k = 1/2
D. Left bar; k = 2
E. Right bar; k = 2
Attachment:
2023-07-27_13-03-41.png [ 8.36 KiB | Viewed 57056 times ]
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27 Aug 2023, 06:57
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Bunuel
7 fuses (3 def, 4 Ndef) are in the box, from which a random sample of 2 fuses is selected.
Left column:
P(0 def) = P(Ndef & Ndef) = 4/7 × 3/6 = 2/7
Middle column:
P(1 def) = P(def & Ndef) + P(Ndef & def) = 3/7 × 4/6 + 4/7 × 3/6 = 4/7
Right column:
P(2 def) = (def & def) = 3/7 × 2/6 = 1/7
According to the probabilities above, the ratio of the heights of the columns should be:
Left : Middle : Right = 2 : 4 : 1
We see that, in the graph, the heights of the left and right columns are in the correct ratio of 2 : 1. So, the height of the middle column should be changed.
If we double the height of the middle column by multiplying its height by the factor k = 2, then all three heights will be in the correct ratio.
Answer: B
03 Aug 2023, 04:41
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Bunuel
Probability of selecting 0 defective bulbs = \(\frac{^4C_2}{^7C_2}\) = \(\frac{4*3}{7*6}\)
Probability of selecting 1 defective bulbs = \(\frac{^4C_1*^3C_1}{^7C_2}\) = \(\frac{4*3*2}{7*6}\)
Probability of selecting 2 defective bulbs = \(\frac{^3C_2}{^7C_2}\) = \(\frac{3*2}{7*6}\)
Therefore the middle bar is incorrect. We need to multiply the current value by a factor of 2 to obtain the correct value.
Option B
