GATE ECE 2014 Set 2 | GA | Question: 4

Question

A regular die has six sides with numbers $1$ to $6$ marked on its sides. If a very large number of throws show the following frequencies of occurrence: $1 \rightarrow 0.167$; $2  \rightarrow 0.167$; $3 \rightarrow 0.152$; $4 \rightarrow 0.166$; $5 \rightarrow 0.168$; $6 \rightarrow 0.180$. We call this die

• A. irregular
• B.  biased
• C. Gaussian
• D. insufficient

Comments

The die is biased because each face does not show up with the same probability. For a fair die, each side should appear about 16.67% of the time, but here, some sides have slightly higher or lower chances (like 0.180 for side 6 and 0.152 for side 3). This difference means some faces are more likely than others, making the die biased.

It’s not "insufficient" because the probabilities add up to 1, which includes all possible outcomes. This means we have enough information to understand how the die behaves.

Answer 1

For a very large number of throws, the frequency should be same for an unbiased die.

But given frequencies are not same, hence the die is biased.Hence, option B.

Comments

@Mk Utkarsh,

I think when the probabilities plotted against the number on the die will give a bell shaped curve then we can call it a Gaussian distribution (Normal distribution). Here it is not the case. Normal distribution is a distribution for continuous random variable. Here the random variable takes discrete values.

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MiNiPanda thanks i asked this when i was unaware of these terms  :p

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@MiNiPanda

Yes here we have discrete distribution ..where Random Variable assigned value as number appearing as outcome.Moreover it is asked

 We call this die..

How can we call a die as gaussian :) ..it is distribution of random variable which will be gaussian.