Probability Question 168
Question: A problem in mathematics is given to three students, A, B, C and their respective probability of solving the problem is $ \frac{1}{2} $ , $ \frac{1}{3} $ and $ \frac{1}{4} $ . Probability that the problem is solved is
Options:
A) $ \frac{3}{4} $
B) $ \frac{1}{2} $
C) $ \frac{2}{3} $
D) $ \frac{1}{3} $
Show Answer
Answer:
Correct Answer: A
Solution:
$ P(E_1)=\frac{1}{2},P(E_2)=\frac{1}{3}$ and $P(E_3)=\frac{1}{4}; $
$ P(E_1UE_2UE_3)=1-P(\overline{E_1})P(\overline{E_2})P(\overline{E_3}) $
$ =1-( 1-\frac{1}{2} )( 1-\frac{1}{3} )( 1-\frac{1}{4} )=\frac{3}{4} $
BETA
