Statistics And Probability Question 89
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} $
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Answer:
Correct Answer: A
Solution:
- [a] $ P(E_1)=\frac{1}{2},P(E_2)=\frac{1}{3}andP(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
