Answer:
42.1875% probability that the student gets all three questions wrong
Step-by-step explanation:
For each question, there are only two possible outcomes. Either the student gets it wrong, or he does not. The probability of the student getting a question wrong is independent of other questions. So we use the binomial probability distribution to solve this question.
Binomial probabily distribution:
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
On a multiple-choice test, each question has 4 possible answers.
One of these options is correct and the other 3 are wrong. We want to find the probability of getting questions wrong. So
Three question:
This means that
What is the probability that the student gets all three questions wrong?
This is P(X = 3).
42.1875% probability that the student gets all three questions wrong