A test consists of 10 true or false questions. To pass the test a student must answer at least eight questions correctly. If the student guesses on each question, what is the probability that the student will pass the test

Step-by-step explanation:

Here, the total number of questions in the test   = 10

The minimum correct answers needed to pass the test  = 8 or more

⇒  n ≥ 8

Now, since there are only 2 options for each question:

So, the probability of answering it right   =  

And the probability of answering it wrong    =  

Now, let us use the Binomial Distribution Formula here:

Now, solving for x = 8 , 9 and 10

When x  = 8 , P(8) is given as :

When x  = 9 , P(9) is given as :

When x  = 10 , P(10) is given as :

Now, adding the 3 probabilities, we get:

(P  ≥ 8) =  P(8) + P(9) + P(10) =  0.0439 + 0.009 + 0.0009 = 0.0538

or, (P  ≥ 8) =  0.0538

Hence,  the probability that the student will pass the test is 0.0538.

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step-by-step explanation:

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