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A student takes a 20-question, true/false exam and guesses on each question. Find the probability of passing if the lowest passing grade is 15 correct out of 20.

Answer :

The required probability is given below:

Required probability = 0.021

The event is not likely to occur because it is less than 0.05.

For the given scenario, we have to use the binomial distribution to find the required probability.

For the given scenario of the binomial distribution, we have

n 20

p = 0.50

For the given scenario, each question has two options such as true or false, so the probability of success is ½ or 0.50.

We have to find the probability of passing if the lowest passing grade is 15 correct out of 20.

That is, we have to find P(X≥ 15).

We have

P(X≥ 15) = 1 - P(X ≤ 14)

We have

P(X ≤ 14) 0.979305

So, we have

P(X15)=1-P(X<14)

1-0.979305

0.020695

≈ 0.021

The event is not likely to occur because it is less than 0.05. That is, the event is unusual.

The required probability is given below:

Required probability = 0.021

The event is not likely to occur because it is less than 0.05.

Question

A student takes a 20-question, true/false exam and guesses on each question. Find the probability of passing if the lowest passing grade is 15 correct out of 20. Would you consider this event likely to occur? Explain your answer. 0.021; no, it’s only about a 2% chance.

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