Pb.20 What is the probability that Hiroko....will be chosen

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Discussion Overview

The discussion revolves around a probability problem concerning the selection of a representative from a History Club, specifically focusing on the probability that a member named Hiroko will be chosen, given that three officers are excluded from selection. The scope includes mathematical reasoning and informal exploration of problem-solving approaches.

Discussion Character

  • Mathematical reasoning
  • Exploratory
  • Debate/contested

Main Points Raised

  • One participant proposes that the probability Hiroko will be chosen is calculated by subtracting the number of officers (3) from the total members (35), leading to 32 eligible members.
  • Another participant agrees with the calculation, asserting that since there are 32 valid options, the probability of selecting any one member, including Hiroko, is 1/32.
  • A different participant expresses a desire for the problem to be more complex, indicating a potential interest in deeper exploration of the topic.
  • One participant mentions that they sometimes post problems to gather different viewpoints and insights, suggesting an interest in learning from the community.

Areas of Agreement / Disagreement

Participants generally agree on the calculation leading to a probability of 1/32 for Hiroko being chosen, but there is an underlying tension regarding the complexity of the problem and the methods of solving it.

Contextual Notes

Some participants express uncertainty about the "approved and official method" for solving probability problems, indicating that there may be multiple approaches or interpretations of the problem.

Who May Find This Useful

Individuals interested in probability theory, informal problem-solving strategies, or those seeking community insights on mathematical reasoning may find this discussion beneficial.

karush
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The 35 member History Club is meeting to choose a student government representative. \item The members decide that the representative, who will be chosen at random, CANNOT be any of the 3 officers of the club.
What is the probability that Hiroko, who is a member of the club but NOT an officer, will be chosen?

a. $0 \quad$ b. $\dfrac{4}{35} \quad$ c. $\dfrac{1}{35} \quad$ d. $\quad {\dfrac{1}{3}}\quad$ e. $\dfrac{1}{32}$
I chose e
ok, I don't know the approved and official method to solve this
just subtracted 3 from 35 and that was the probability

I'm going to study (on my own, not in a class) probability and statistics for february march and april
so I will be posting a lot here
 
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First, no matter what your teachers tell you, there is NO "approved and official method" of solving a problem. As long as you get the right answer and know that you have the right answer, that's sufficient! Logical thinking gives you that.

Second, since the three officers of the club are not eligible to serve, there are 35- 3= 32 who are. That is the logical thinking you were doing, perhaps without realizing it. That is the reason you subtracted 3, for three officers who are not allowed to serve. The next step is two realize that, since all of the remaining 32 people are "equally likely" to be selected, and probabilities must add to 1, each must have probability 1/32.

Finally, stop bragging about living in Hawaii and surfing in January!
 
actually i have never surfed in Hawaii
even though i live just a short drive from the famous pipeline

Anyway
 
Hi karush!

Part of me wants this problem to be more complicated than it seems, but I agree with you that it should be (e). There are 32 valid options to choose from at random, so 1/32 of a single person being chosen from that pool.
 
well sometimes i post a problem,,, even though i know how to solve it just to get more view points
lots of little unknown tricks and tips out there..

yeah I am not in a class room so there is no father figure..
 

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