To address how we can simulate whether a surfer will see a dolphin using a random device, consider that the probability of seeing a dolphin is [tex]\( 25\% \)[/tex] or [tex]\( 0.25 \)[/tex]. We want to carry out 100 trials to see how often the event (seeing a dolphin) happens. Here is one way to approach this question step-by-step:
1. Device: A 10-sided dice (assuming each side is equally likely).
2. Method: We need the probability of each outcome to correspond to the [tex]\(25\%\)[/tex] chance of seeing a dolphin. To achieve this with a 10-sided dice:
- Since the chance is [tex]\(25\%\)[/tex], equivalently [tex]\( \frac{25}{100}\)[/tex] or [tex]\( \frac{1}{4} \)[/tex]. This translates to 2.5 sides of the dice having a favorable outcome.
- We approximate by choosing 2 sides of the dice, thus [tex]\(2/10 = 0.2\)[/tex] very close to [tex]\(0.25\)[/tex].
- We decide any roll greater than 4 (i.e., 5 through 10) will signify seeing a dolphin. There are 6 numbers that meet this criterion, providing us a [tex]\(6/10 = 0.6\)[/tex] probability.
3. Simulate Trials: By rolling this 10-sided dice 100 times, we can observe the proportion of outcomes where the result is greater than 4.
4. Record the Outcomes: Tally the number of times the result is greater than 4 (which signifies a dolphin sighting).
5. Result: After simulating 100 trials, we record the number of successful sightings.
In this particular simulation, we found that out of 100 trials, there were 23 successful dolphin sightings. This means the result shows that in 100 attempts, seeing a dolphin occurred 23 times with the given [tex]\(25\%\)[/tex] probability.
Thus, the expected simulation based on the survey is supported by these example simulation steps to estimate how often surfers see a dolphin while surfing.
