The probability of rolling any number on weighted 6-sided die, with fa

Question

The probability of rolling any number on weighted 6-sided die, with faces number 1 through 6, is directly proportional to the number rolled. What is the probability of getting 5, if the die is rolled only once ?
A. 1/6
B. 5/6
C. 5/16
D. 5/21
E. None of these

KarishmaB · Accepted Answer

"Weighted" 6 sided die means it is not a "fair" 6 sided die. On a fair die, the probability of getting any number is the same. On a weighted die, the probabilities for different numbers are different.

We are given that the probability is "directly proportional to the number rolled". So if probability of rolling 1 is a, probability of rolling 2 is 2a and that of rolling 3 is 3a and so on...

The total probability must be 1 so 
a + 2a + 3a + 4a + 5a + 6a = 1
a = 1/21

Probability of rolling a 5 is 5a = 5/21

Answer (D)

MahmoudFawzy · Answer

The ratio of the probability of the  6  faces from  1  to  6  is  1:2:3:4:5:6  with total of  21 
so the probability of getting  5  =  \frac{5}{21}

CareerGeek · Answer

Given, weightage of number 1 turning up is 1, number 2 turning up is 2 and so on ...
—> Total weightage of any number turning up = 1 + 2 + 3 + 4 + 5 + 6 = 21

Favourable = number 5 turns up = 5

Required Probability = 5/21

IMO D

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globaldesi · Answer

Given total probability is 1+2+3+4+5+6 = 21
probability of 5 is thus 5/21 hence D

Hea234ven · Answer

I am not getting the answer explanation clearly. can anyone please explain what does it mean by weighted sided die? And how did you come to the total possible outcome 21?

Hea234ven · Answer

Thanks for the explanation. Got it now...

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shohan2722 · Answer

I'm not being able to understand what a weighted die means. Can you explain a little further maybe with an example?

Regor60 · Answer

An unweighted die is one in which each of the 6 faces has an equal probability of turning up. So with 6 faces, each has 1/6 chance.

A weighted die is one in which certain faces have a probability less than 1/6 and others greater than 1/6.

In this question the weights are assigned by the number on the die. So 6 has 6 times the chance of showing up than 1, for example, or 3 has a 50% greater chance than 2.

The response above shows how these weights are added up and then each die has a probability of its number divided by the sum of the weights.

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KarishmaB · Answer

Normally our die questions involve a "fair die". All the 6 sides are exactly the same except for the numbers written on them. One side has 1 written on it (or one dot on it), another side has 2 on it (or 2 dots) etc. 
A weighted die is not fair. The probability of one side coming up is different from the probability of another side. Say the sides are of different weights so the die is most likely to fall on the heaviest side. If the side opposite to it has 6 on it, the probability of getting a 6 will be more than the probability of getting any other number etc.
The question tells us that the probability of each side is proportional to the number on it. So if probability of getting 1 is n, probability of getting 2 is 2n, of getting 3 is 3n and so on. 
Since total probability is 1, we get n + 2n + 3n + 4n + 5n + 6n = 21n = 1

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The probability of rolling any number on weighted 6-sided die, with fa

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