Question

A die was rolled 120 times and the number of times 6 came up was noted. If the experimental probability calculated from this information is 1/3, then how many times 6 came up ?

• A. 20
• B. 30
• C. 40
• D. 60

Hint:

An experimental probability of \(\frac{1}{3}\) means that the event happens exactly once every 3 trials.
For 120 trials, it must happen:
\[ 120 \times \frac{1}{3} = 40 \text{ times} \]
This is a straightforward multiplication that can be done mentally.

Answer 1

The Correct Option is C

Step 1: Read the experimental probability as a simple fraction of trials.
A probability of $\frac{1}{3}$ out of 120 rolls means that, on average, 1 out of every 3 rolls gave a six.
Step 2: Use the unitary method to count actual sixes.
Splitting 120 rolls into groups of 3, we get \[ \frac{120}{3} = 40 \text{ groups} \] and each group contributes exactly one six under this experimental probability, so there are 40 sixes in total.
Step 3: Conclude. \[ \boxed{40} \]