Researchers have found that children as young as two year old toddlers

Question

Researchers have found that children as young as two year old toddlers use mathematical concepts such as probability to understand the world around them and make decisions accordingly. In an experiment conducted to study such behaviour, toddlers observed an experimenter play a game with two different colored buttons. The pressing of the button would sometimes release a marble and sometimes not. When these toddlers were asked to play the same game, 23 out of 32 toddlers chose to press the button that was more successful in generating a marble.

Which of the following, if true, is important to rule out the possibility that the toddlers made a choice purely based on frequency, i.e. the number of times a button returned marbles, rather than probability?

A. The toddlers who chose the button that returned a marble fewer number of times were measured to have the same IQ as the ones who chose the other button.

B. None of the toddlers were found to have color-blindness and could differentiate between the two buttons on the basis of their colors.

C. During the experimenter's turn at the game, both the buttons generated a marble the same number of times, though the number of attempts for each button varied significantly.

D. 19 out of 23 toddlers who chose the button that was more successful in generating marbles belonged to families in which one of the parents was a Mathematics teacher.

E. Both the buttons released marbles with the same number of unsuccessful attempts between two successful ones.

SonalSinha803 · Answer

A. The toddlers who chose the button that returned a marble fewer number of times were measured to have the same IQ as the ones who chose the other button. - talks about IQ, therefore, irrelevant.

B. None of the toddlers were found to have color-blindness and could differentiate between the two buttons on the basis of their colors. - irrelevant

C. During the experimenter's turn at the game, both the buttons generated a marble the same number of times, though the number of attempts for each button varied significantly. - Talks about frequency and attempts made. Hold

D. 19 out of 23 toddlers who chose the button that was more successful in generating marbles belonged to families in which one of the parents was a Mathematics teacher. - irrelevant

E. Both the buttons released marbles with the same number of unsuccessful attempts between two successful ones -

indicates that the probability is same. So then, how can the toddler decide on the basis of probability. Thus, I eliminated this.

IMO C, though not 100% sure.

OA ??

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Masterscorp · Answer

C is the correct choice imo. The question asks us to rule out the possibility that the frequency influenced the toddlers' decision. C tells us that the frequency of both buttons was the same, hence it couldn't be the deciding factor. Hope that helps

debabrata1234 · Answer

Researchers have found that children as young as two year old toddlers use mathematical concepts such as probability to understand the world around them and make decisions accordingly. In an experiment conducted to study such behaviour, toddlers observed an experimenter play a game with two different colored buttons. The pressing of the button would sometimes release a marble and sometimes not. When these toddlers were asked to play the same game, 23 out of 32 toddlers chose to press the button that was more successful in generating a marble.

Which of the following, if true, is important to rule out the possibility that the toddlers made a choice purely based on frequency, i.e. the number of times a button returned marbles, rather than probability?

A. The toddlers who chose the button that returned a marble fewer number of times were measured to have the same IQ as the ones who chose the other button.

B. None of the toddlers were found to have color-blindness and could differentiate between the two buttons on the basis of their colors.

C. During the experimenter's turn at the game, both the buttons generated a marble the same number of times, though the number of attempts for each button varied significantly.

D. 19 out of 23 toddlers who chose the button that was more successful in generating marbles belonged to families in which one of the parents was a Mathematics teacher.

E. Both the buttons released marbles with the same number of unsuccessful attempts between two successful ones.

negating the main point:
kid used probabilty not frequency to press the buttons
given that a) 50% chance of getting a marble from each button.

pre-think:
1. when probabiility is same , kid cannot use it to decide.

look at the options:
A. The toddlers who chose the button that returned a marble fewer number of times were measured to have the same IQ as the ones who chose the other button.
even if kid have different IQ, it doesnot imply how they decided. hence irrelevant.

B. None of the toddlers were found to have color-blindness and could differentiate between the two buttons on the basis of their colors.
even if both buttons are same color, they still use counting to calculate the frrquency or probability. hence it is irrelevant

C. During the experimenter's turn at the game, both the buttons generated a marble the same number of times, though the number of attempts for each button varied significantly. 
lets say a -> 10 attempts and b-> 5 attempts
as per c successful attempts for both are same , lets success = 2 , then probaility for each is different. this will help the 
kid to select high probability button.hence negating it , probability is different, sometimes a>b , sometimes b>a depending upon no of successful attempts of each kid. hence probability cannot be used.

D. 19 out of 23 toddlers who chose the button that was more successful in generating marbles belonged to families in which one of the parents was a Mathematics teacher. 
even if parents are mathematicians, it doesnot say anything. hence irrelevant.

E. Both the buttons released marbles with the same number of unsuccessful attempts between two successful ones.
if successful and unsuccessful attempts of both are same,then there is a chance of 50% proabaility in each case.
but negating will say they have different probabilty. hence it is opposit. hence incorrect

PSKhore · Answer

The answer is C. 
 To distinguish between frequency and probability, the key is to isolate frequency as a factor. If both buttons produced the same number of marbles but with varying attempts during the experimenter's turn, then the toddlers' choice of the more successful button (23 out of 32) is likely based on probability rather than just the sheer number of times the marble was released.

Explanation :
Probability vs. Frequency:
Probability is the likelihood of an event happening, while frequency is how often it has happened in the past. If both buttons generated marbles the same number of times (frequency), but one did it in fewer attempts (higher probability), the toddlers' choice for the more successful button would indicate they understood probability.

Why other options are incorrect:

A: IQ is a measure of intelligence and does not directly relate to the understanding of probability. If all toddlers have the same IQ, it doesn't eliminate the possibility that they are choosing based on frequency.
B: Color blindness is irrelevant if the toddlers can differentiate between the buttons. The question is about probability vs. frequency, not color perception.
D: Parental occupation as a mathematics teacher could introduce a bias, but it doesn't explain whether the toddlers themselves understand probability. Some children of mathematicians might choose based on frequency.
E: Equal number of unsuccessful attempts between successful ones does not explain the toddlers' choice. This option is not relevant to the experiment.
 
 Key takeaway : Option C directly addresses the core issue of differentiating probability from frequency in the toddlers' decision-making process.

Source: AI Overview

Vivek1707 · Answer

Question understanding ---> The questions is asking which one of the following if true will help to rule out the possibility that the toddlers made a choice purely based on frequency and not on probability. In other words which of the answer choices will strengthen the fact that the toddlers made a choice based on probability and not on frequency.

A frequency based toddler would say ---> Ok this button gave more marbles to I would choose this 
A probability based toddler would say ---> Ok this button is more successful i.e. even thought it took more attempts, it gave more marbles per attempt i.e. the % of success or the rate of success (probability) was higher

Option C if the toddlers saw that that the number of attempts varied but the marbles were the same . A probability based toddler would choose the one more successful (since its given in the prompt that this happened). Hence a frequency based explanation will not be sufficient for this hence this rules out frequency based explanation --> correct

E - This doesn't explain whether a toddler would choose a button for sheer frequency or for sheer success rate i.e. probability. It does not rule out frequency based reasoning. The toddler could have chosen the button that gives more marbles.

namanqqkm · Answer

I think E has to do with saying probability is same, and if probability is same then it becomes irrelevant to say or rule out probability. C says frequency played a role, and therefore its the correct ans.

and if you think B as a choice, the even if the children were color blind or no different coloured buttons where used, the children's could have just followed what previous child did, also this option doesn't tell us anything about frequency or probability hence its an open ended option.

miag · Answer

Hi,

Your logic for rejecting E) is not entirely correct:
E) doesn't establish = probability. E) is incorrect because it describes pattern regularity, not probability. It also doesn't allow us to rule out frequency.
B) Your understanding is correct: It has nothing to do with frequency vs probability. It doesn’t rule out imitation, counting, or pattern-following.

Hope this helps!

Researchers have found that children as young as two year old toddlers

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