Question

you want to do an experiment. on any given day, there is a 30% chance that your participant won't show up. in addition, there is a 10% chance that the stimulus presentation software won't work. there is also a 5% chance that there is a problem with saving the data and a 2% chance that there are other problems like experimenter error. for the sake of simplicity, you can assume that all these events are independent. what is the probability that you will be able to do a successful experiment (be able to record useful data) on any given day?

Answer 1

The probability of a successful experiment on any given day, considering all independent events, is approximately 61.58%.

Step-by-step explanation:

To calculate the probability of a successful experiment you must consider all the independent events that can prevent it from happening: the participant not showing up, issues with the software, problems saving the data, and other potential issues. Since these events are independent, you need to multiply the probability of each one not happening to find the overall probability of a successful experiment.

The probability that the participant will show up is 70% (100% - 30% chance of not showing up), the software will work 90% of the time (100% - 10% chance of not working), the data will save 95% of the time (100% - 5% chance of issues), and there will be no experimenter error 98% of the time (100% - 2% chance of error). You then multiply these probabilities to get the overall probability of a successful experiment.

• Probability of participant showing up: 0.70
• Probability of software working: 0.90
• Probability of data saving: 0.95
• Probability of no other errors: 0.98

Multiplying these together: 0.70 * 0.90 * 0.95 * 0.98 = 0.6158 or 61.58%

Therefore, the probability of being able to do a successful experiment on any given day is approximately 61.58%.