Probability Question 9
Question: In an examination, the probability of a candidate solving a question is $ \frac{1}{2}. $ Out of given 5 questions in the examination, what is the probability that the candidate was able to solve at least 2 questions?
Options:
A) $ \frac{1}{64} $
B) $ \frac{3}{16} $
C) $ \frac{1}{2} $
D) $ \frac{13}{16} $
Show Answer
Answer:
Correct Answer: D
Solution:
$ P{{=}^{5}}C_2{{( \frac{1}{2} )}^{2}}{{( \frac{1}{2} )}^{3}}{{+}^{5}}C_3{{( \frac{1}{2} )}^{3}}{{( \frac{1}{2} )}^{3}} $
$ {{+}^{5}}C_4{{( \frac{1}{2} )}^{4}}{{( \frac{1}{2} )}^{1}}{{+}^{5}}C_2{{( \frac{1}{2} )}^{5}}{{( \frac{1}{2} )}^{0}} $
$ ={{( \frac{1}{2} )}^{5}}[ ^{5}C_2{{+}^{5}}C_3{{+}^{5}}C_4{{+}^{5}}C_5 ] $
$ =\frac{1}{3^{2}}\times 26=\frac{13}{16}. $
BETA
