You take a quiz with 6 multiple choice questions. After you studied, you estimated that you would have about an 80% chance of getting any individual question right. What are your chances of getting them all right? The random numbers below represent a simulation with 20 trials. Let 0-7 represent a correct answer and let 8-9 represent an incorrect answer.
To calculate your chances of getting all questions right, we need to consider the probability of getting each individual question right and multiply them together.
Since you estimated an 80% chance of getting any individual question right, the probability of getting a question wrong would be 1 - 0.80 = 0.20.
Let's use p to represent the probability of getting a question right and q to represent the probability of getting a question wrong. In this case, p = 0.80 and q = 0.20.
To find the probability of getting all questions right, we multiply the probabilities together:
0.80 * 0.80 * 0.80 * 0.80 * 0.80 * 0.80 = 0.262144
Therefore, your chances of getting all 6 questions right are approximately 26.21%.
The random numbers given in the simulation are not necessary to calculate the probability of getting all questions right. They would be used if you want to simulate multiple trials and observe different outcomes.
To calculate the chances of getting all the questions right, we can use the concept of independent events.
Since there are 6 questions and each question has an 80% chance of being answered correctly, we can calculate the probability of getting all the questions right by multiplying the individual probabilities together.
Probability of getting one question right = 80% = 0.80
Probability of getting all questions right = (0.80)^6 = 0.262144
Therefore, the chances of getting all 6 questions right are approximately 26.21% or 0.262144.
Please note that the random numbers provided for simulation are not required for calculating the probability but can be used for conducting a simulation or verifying the calculated probability with the observed results.