Respuesta :
The probability of any student passing the given test is 0.0538.
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 = [tex](\frac{1}{2} ) = 0.5 = p[/tex]
And the probability of answering it wrong = [tex](\frac{1}{2} ) = 0.5 = q[/tex]
Now, let us use the Binomial Distribution Formula here:
[tex]P(x) = ^nC_x p^xq^{(n-x)}[/tex]
Now, solving for x = 8 , 9 and 10
When x = 8 , P(8) is given as :
[tex]P(8) = ^{10}C_8 (0.5)^8(0.5)^{(10-8)} = 45\times (0.5)^8(0.5)^2 = 0.0439[/tex]
When x = 9 , P(9) is given as :
[tex]P(9) = ^{10}C_9 (0.5)^9(0.5)^{(10-9)} = 10\times (0.5)^9(0.5)^1 = 0.009[/tex]
When x = 10 , P(10) is given as :
[tex]P(10) = ^{10}C_{10} (0.5)^10(0.5)^{(10-10)} = 10\times (0.5)^{10}(0.5)^0 = 0.0009[/tex]
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.
