Probability Question 56
Question: An experiment succeeds twice as often as it fails. Find the probability that in 4 trials there will be at least three success
[AMU 1999]
Options:
A) $ \frac{4}{27} $
B) $ \frac{8}{27} $
C) $ \frac{16}{27} $
D) $ \frac{24}{27} $
Show Answer
Answer:
Correct Answer: C
Solution:
Probability of failure = $ \frac{1}{3} $
Probability for getting success $ =\frac{2}{3} $
Required probability $ ={{}^{4}}C_4{{( \frac{2}{3} )}^{4}}{{( \frac{1}{3} )}^{0}}+{{}^{4}}C_3{{( \frac{2}{3} )}^{3}}( \frac{1}{3} ) $
$ ={{( \frac{2}{3} )}^{4}}+4{{( \frac{2}{3} )}^{3}}( \frac{1}{3} )=\frac{16}{27} $ .
BETA
