Question

The mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on one face is

• A. $5$
• B. $\frac{8}{3}$
• C. $1$
• D. $2$

Hint:

To compute the mean of a die throw quickly, simply sum up the values written on every single face and divide by the total number of faces (6): $\text{Mean} = \frac{1+1+1+2+2+5}{6} = \frac{12}{6} = 2$. This avoids working with fractions entirely!

Answer 1

The Correct Option is D

Step 1: Build the probability distribution.
The die shows 1 on three faces, 2 on two faces, and 5 on one face, over six faces total.
Step 2: Assign probabilities.
$P(1)=\dfrac{3}{6}=\dfrac12$, $P(2)=\dfrac{2}{6}=\dfrac13$, $P(5)=\dfrac{1}{6}$. These add to 1, so the distribution is valid.
Step 3: Recall the mean formula.
The mean (expected value) is $\mu=\sum x_i P(x_i)$.
Step 4: Multiply each value by its probability.
$1\cdot\dfrac12=\dfrac12$, $2\cdot\dfrac13=\dfrac23$, $5\cdot\dfrac16=\dfrac56$.
Step 5: Use a common denominator of 6.
$\dfrac12=\dfrac36$, $\dfrac23=\dfrac46$, $\dfrac56=\dfrac56$.
Step 6: Add them up.
$\mu=\dfrac{3+4+5}{6}=\dfrac{12}{6}=2$, matching option (4).
\[ \boxed{\mu=2} \]