Question

Asked Nov 10, 2019

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A die is loaded in such a way that the probability of each face turning up is proportional to the number of dots on that face. (For example, a six is three times as probable as a two.) What is the probability of getting an even number in one throw?

Step 1

The probability of each face turning up is proportional to the number of dots on that face so,

The probability of getting ** 1** is

The probability of getting ** 2** is

The probability of getting **3** is *3p*

The probability of getting **4 **is *4p*

The probability of getting **5** is *5p *

and The probability of getting **6** is *6p.*

Since by the probability rule, sum of probabilities of the all the possible outcomes is equal to **1**. So

** **

Step 2

The probability of getting an even number in one throw = probability of getting **2** + probability...

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