Probability Question 295
Question: The probability that a man can hit a target is $ \frac{3}{4} $ . He tries 5 times. The probability that he will hit the target at least three times is
[MNR 1994]
Options:
A) $ \frac{291}{364} $
B) $ \frac{371}{464} $
C) $ \frac{471}{502} $
D) $ \frac{459}{512} $
Show Answer
Answer:
Correct Answer: D
Solution:
We have $ p=\frac{3}{4}\Rightarrow q=\frac{1}{4} $ and $ n=5 $
Therefore required probability $ ={}^{5}C_3{{( \frac{3}{4} )}^{3}}{{( \frac{1}{4} )}^{2}}+{}^{5}C_4{{( \frac{3}{4} )}^{4}}( \frac{1}{4} )+{}^{5}C_5{{( \frac{3}{4} )}^{5}} $
$ =\frac{10.27}{4^{5}}+\frac{5.81}{4^{5}}+\frac{243}{4^{5}}=\frac{270+405+243}{1024}=\frac{459}{512}. $
BETA
