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: Understanding the Question:
This question is from the topic of Probability, specifically concerning experimental (or empirical) probability.
We are given the total number of trials and the calculated experimental probability of an event. We need to find the number of times that specific event occurred.

Step 2: Key Formula or Approach:
Experimental probability of an event is defined as:
\[ \text{Experimental Probability} = \frac{\text{Number of times the event occurred}}{\text{Total number of trials}} \]

Step 3: Detailed Explanation:
Let \(x\) be the number of times the face with '6' came up.
We are given:
- Total number of rolls (trials) = 120
- Experimental probability of getting a '6' = \(\frac{1}{3}\)
Using the probability formula:
\[ \text{Experimental Probability} = \frac{x}{120} \]
Substitute the given value:
\[ \frac{1}{3} = \frac{x}{120} \] Solve for \(x\) by multiplying both sides by 120:
\[ x = \frac{120}{3} \]
\[ x = 40 \]
Therefore, the number '6' came up 40 times.

Step 4: Final Answer:
The number 6 came up 40 times.