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29 Jul 2024, 08:10
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In a science experiment, a mouse is placed in a labyrinth with two different treats hidden in it. What is the probability that the mouse will find neither of the treats?
(1) The probability that the mouse will find only one of the two treats is \(\frac{1}{5}\).
(2) The probability that the mouse will find both treats is \(\frac{3}{10}\).
(1) The probability that the mouse will find only one of the two treats is \(\frac{1}{5}\).
(2) The probability that the mouse will find both treats is \(\frac{3}{10}\).
29 Jul 2024, 08:10
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Official Solution:
In a science experiment, a mouse is placed in a labyrinth with two different treats hidden in it. What is the probability that the mouse will find neither of the treats?
This is an overlapping problem in disguise, so let's treat it as such:
Essentially, we need to find the value of the green box given that the sum of the four colored boxes is 1.
(1) The probability that the mouse will find only one of the two treats is \(\frac{1}{5}\).
The above gives the sum of the values of the red boxes, which is not sufficient to find the value of the green box.
(2) The probability that the mouse will find both treats is \(\frac{3}{10}\).
The above gives the value of the yellow box, which is not sufficient to find the value of the green box.
(1)+(2) Together, we have the combined value of the red boxes (\(\frac{1}{5}\)) and the value of the yellow box (\(\frac{3}{10}\)). Thus, the value of the green box is \(1 - (\frac{1}{5} + \frac{3}{10}) = \frac{1}{2}\). Sufficient.
Answer: C
In a science experiment, a mouse is placed in a labyrinth with two different treats hidden in it. What is the probability that the mouse will find neither of the treats?
This is an overlapping problem in disguise, so let's treat it as such:
Essentially, we need to find the value of the green box given that the sum of the four colored boxes is 1.
(1) The probability that the mouse will find only one of the two treats is \(\frac{1}{5}\).
The above gives the sum of the values of the red boxes, which is not sufficient to find the value of the green box.
(2) The probability that the mouse will find both treats is \(\frac{3}{10}\).
The above gives the value of the yellow box, which is not sufficient to find the value of the green box.
(1)+(2) Together, we have the combined value of the red boxes (\(\frac{1}{5}\)) and the value of the yellow box (\(\frac{3}{10}\)). Thus, the value of the green box is \(1 - (\frac{1}{5} + \frac{3}{10}) = \frac{1}{2}\). Sufficient.
Answer: C
14 Sep 2024, 11:57
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Looks very logical. Using the both statements we can infer the answer:- Here this table method and visualization technique helps to answer this question quickly. A and Not B, B and Not A - Given as 1/5 ( any one of the treats) now , both the probability is given as 3/10 so both together 3/10 + 1/5 is reduced from total probability 1 to find the neither probability
