Maths Olympiad Prep

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Combinatorics Difficulty 2.9 Junior Find the answer

A dormitory of a certain high school senior class has 8 people. In a health check, the weights of 7 people were measured to be 60, 55, 60, 55, 65, 50, 50 (in kilograms), respectively. One person was not measured due to some reasons, and it is known that the weight of this student is between 50 and 60 kilograms. The probability that the median weight of the dormitory members in this health check is 55 is __.

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Given that one person was not measured, and the median weight of the dormitory members is 55, the weight of the person not measured must be between 55 and 60. Using the geometric probability model, the probability that the median weight of the dormitory members is 55 is calculated as follows:
p=60556050=12p = \frac{60-55}{60-50} = \frac{1}{2}
Therefore, the answer is 12\boxed{\frac{1}{2}}.

This problem involves the concept of probability and the use of geometric probability model. It also requires basic arithmetic skills.

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.