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Sagot :
The probability that Justin passes his final exam is 0.0147%
How to determine the probability?
The given parameters are:
- Questions, n = 20
- Pass mark, x = 25
- Number of options = 3
Only one of the options can be correct.
So, the probability that he answers a question correctly is:
p = 1/3
To get a pass mark of 75, he must score at least 15.
So, the probability is represented using:
P(x >= 15) = P(15) + P(16) + ..... + P(20)
Each probability is calculated using:
[tex]P(x) = ^nC_r * p^x *(1 -p)^{n - x}[/tex]
Using the above formula, we have:
P(15) = 0.00012546624
P(16) = 0.0000193115
P(17) = 0.00000223803
P(18) < 0.000001
P(19) < 0.000001
P(20) < 0.000001
When the above probabilities are added, we have:
P(x >= 15) = 0.00014720925
Express as percentage
P(x >= 15) = 0.014720925%
Approximate
P(x >= 15) = 0.0147%
Hence, the probability that Justin passes is 0.0147%
Read more about probability at:
https://brainly.com/question/251701
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