Using the binomial distribution, it is found that there is a 0.0008 = 0.08% probability that she will get a passing score.
For each question, there are only two possible outcomes, either she answers it correctly, or she does not. The probability of answering a question correctly is independent of any other question, which means that the binomial distribution is used to solve this question.
Binomial probability distribution
The parameters are:
- x is the number of successes.
- n is the number of trials.
- p is the probability of a success on a single trial.
In this problem:
- 18 questions, thus
- Guess one of three correct options, thus .
A passing score is <u>at least 13 correct</u>, thus, the probability is:
Then
The others, until P(X = 18), will be approximately 0, thus:
0.0008 = 0.08% probability that she will get a passing score.
A similar problem is given at brainly.com/question/24863377