Probability Question 24
Question: The probability of guessing correctly at least 8 out of 10 answers on a true-false examination is
Options:
A) $ \frac{5}{128} $
B) $ \frac{19}{128} $
C) $ \frac{11}{128} $
D) $ \frac{7}{128} $
Show Answer
Answer:
Correct Answer: D
Solution:
$ p(X\ge 8){{=}^{10}}C_8{{( \frac{1}{2} )}^{8}}{{( \frac{1}{2} )}^{2}}{{+}^{10}}C_9{{( \frac{1}{2} )}^{9}}{{( \frac{1}{2} )}^{1}}{{+}^{10}}C_{10}{{( \frac{1}{2} )}^{10}} $
$ ={{( \frac{1}{2} )}^{10}}{{[}^{10}}C_2{{+}^{10}}C_1{{+}^{10}}C_0]=\frac{56}{8\times 2^{7}}=\frac{7}{128}. $
BETA
