solve by simulating the problem.you have a 5 -question multiple -choice test. each question has four chices. you don't know any of the answers. what is the experimental probility that you will guess exactly three out of five question correctly?
To find the experimental probability of guessing exactly three out of the five questions correctly, you can simulate the problem using a random number generator and a loop.
Here's how you can approach the simulation:
1. Set up a loop that will simulate multiple attempts at guessing the answers. For example, let's say you want to simulate 10,000 attempts.
2. Within the loop, generate a random number from 1 to 4 to represent a guess for each question. Repeat this process for all five questions.
3. Count the number of correct guesses for each attempt.
4. Keep track of the number of attempts that resulted in exactly three correct answers.
5. After completing all the simulated attempts, calculate the experimental probability by dividing the number of attempts with three correct guesses by the total number of attempts.
Now, let's translate these steps into code:
```python
import random
total_attempts = 10000
correct_attempts = 0
for _ in range(total_attempts):
# Simulating guesses for each question
guesses = [random.randint(1, 4) for _ in range(5)]
# Counting the number of correct guesses
correct_guesses = sum(guesses)
# Checking if exactly three answers are correct
if correct_guesses == 3:
correct_attempts += 1
experimental_probability = correct_attempts / total_attempts
```
The `random.randint(1, 4)` function is used to generate a random integer between 1 and 4 (inclusive) for each question. The `sum` function is used to count the number of correct guesses.
By running this code, you will get the experimental probability of guessing exactly three out of five questions correctly based on the simulated results.