Answer:
Q1) The student has a 0.01% probability of passing the test.
Q2) She has a 99.91% probability of passing in the test.
Step-by-step explanation:
For each question, there are only two possible outcomes. Either he gets it correct, or he gets it wrong. So we solve this problem using the binomial probability distribution.
Binomial probability 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 combinatios of x objects from a set of n elements, given by the following formula.
And is the probability of X happening.
For this problem, we have that:
Question 1.
There are 50 questions, so .
The student is going to guess each question, so he has a probability of getting it right.
He needs to get at least 25 question right.
So we need to find .
Using a binomial probability calculator, with and
we get that
.
This means that the student has a 0.01% probability of passing the test.
Question 2.
Now, we need to find with
. So
She has a 99.91% probability of passing in the test.