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30 Aug 2024, 07:23
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Dropdown 1: 12%
Dropdown 2: 18%
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
49% (02:26) correct
51%
(02:52)
wrong
based on 295
sessions
History
Date
Time
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Not Attempted Yet
The pictograph represents various observations drawn from a study conducted on the residents of a city. The three concentric circles represent the pattern of academic degrees obtained by the residents of the city. Any person carrying a bachelor's degree also carries a high school degree, and any person carrying a master's degree also carries a bachelor's degree and high school degree. The fourth circle on the left represents the status of an ‘own house’ for the residents of the city. The legends A, B, C, D, E, F, and G represent the percentage of residents in the respective categories.
Use the dropdown menus to complete the statements accurately, using the information provided in the diagram.
If a resident of the city is chosen randomly, the probability that he/she completed a bachelor's degree as well as owns a house is
Percentage of the residents of the city who do not carry a high school degree and do not own a house is
The pictograph represents various observations drawn from a study conducted on the residents of a city. The three concentric circles represent the pattern of academic degrees obtained by the residents of the city. Any person carrying a bachelor's degree also carries a high school degree, and any person carrying a master's degree also carries a bachelor's degree and high school degree. The fourth circle on the left represents the status of an ‘own house’ for the residents of the city. The legends A, B, C, D, E, F, and G represent the percentage of residents in the respective categories.
Use the dropdown menus to complete the statements accurately, using the information provided in the diagram.
If a resident of the city is chosen randomly, the probability that he/she completed a bachelor's degree as well as owns a house is
Percentage of the residents of the city who do not carry a high school degree and do not own a house is
ShowHide Answer
Official Answer
Dropdown 1: 12%
Dropdown 2: 18%
30 Aug 2024, 23:31
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dhamsha2
Explanation
I.
Percentage of people who completed a bachelor's degree as well as own a house = B + C = 5 + 7 = 12%.
So, the required probability will be 12%/100% = 12%
Hence, 12% is the correct answer choice.
II.
Percentage of people who do not carry a high school degree and do not own a house = All those outside of A + B + C + D + E + F + G = outside of 82% = 18%
Hence, 18% is the correct answer choice.
An interesting discussion:
A student once wrote to us mentioning that the answer to the first part of the question should have been 5% since the question asks for the probability that the resident has completed a bachelor’s degree AND owns a house, and it would have made sense to add the probabilities if the question asked for the probability that the resident has completed a bachelor’s degree OR owns a house.
Can you figure out the flaw in the reasoning?
There are two mistakes in the reasoning:
1. The above reasoning does not take into account that the question specifies “any person carrying a master’s degree also carries a bachelor’s degree” and hence the resident group “C” also has completed a bachelor’s degree AND owns a house.
2. The terms “AND” and “OR” in the context of probabilities of events seem to have been incorrectly interpreted in the above reasoning. The probability of event X “AND” Y refers to the probability of both events X and Y happening together. The probability of event X “OR” Y refers to the probability of at least one of the events occurring. Below are a few examples of probabilities of various events based on the above example:
• Probability that the resident has completed a bachelor’s degree = (C + B) + (E + F)
• Probability that the resident owns a house = G + (C + B)
• Probability that the resident has completed a bachelor’s degree AND owns a house = (C + B)
• Probability that the resident has completed a bachelor’s degree OR owns a house = G + (C + B) + (E + F)
General Discussion
