Question

A die is rolled so that the probability of face $i$ is proportional to $i,\{i=1,2,.....6\}$. The probability of an even number occurring when the die is rolled, is

• A. $\frac{7}{4}$
• B. $\frac{4}{7}$
• C. $\frac{5}{7}$
• D. None of these

Answer 1

Answer: (B)

$\frac{4}{7}$

Let the probability $i$ is $k$

Then, Probability of getting $1=k$

Probability of getting $2=2k$

Probability of getting $3=3k$

Probability of getting $4=4k$

Probability of getting $5=5k$

Probability of getting $6=6k$

Probability of an even number occuring is,

$=\frac{P\left(2\right)+P\left(4\right)+P\left(6\right)}{Totalprobability}$

$=\frac{2k+4k+6k}{k+2k+3k+4k+5k+6k}=\frac{12}{21}=\frac{4}{7}$