Statistics And Probability Question 124
Question: If odds against solving a question by three students are 2 : 1, $ 5:2 $ and $ 5:3 $ respectively, then probability that the question is solved only by one student is
[RPET 1999]
Options:
A) $ \frac{31}{56} $
B) $ \frac{24}{56} $
C) $ \frac{25}{56} $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
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The probability of solving the question by these three students are $ \frac{1}{3},\frac{2}{7} $ and $ \frac{3}{8} $ respectively. $ P(A)=\frac{1}{3} $ ; $ P(B)=\frac{2}{7} $ ; $ P(C)=\frac{3}{8} $ Then probability of question solved by only one student $ =P(A\,\bar{B}\,\bar{C}\, $ or $ \bar{A}\,B\,\bar{C} $ or $ \bar{A}\,\bar{B}\,C) $ $ =P(A)P(\bar{B})P(\bar{C})\,+\,P(\bar{A})P(B)\,P(\bar{C})\,+P(\bar{A})\,P(\bar{B})\,P\,(C) $ $ =\frac{1}{3}.\frac{5}{7}.\frac{5}{8}+\frac{2}{3}.\frac{2}{7}.\frac{5}{8}+\frac{2}{3}.\frac{5}{7}.\frac{3}{8} $ $ =\frac{25+20+30}{168} $ $ =\frac{25}{56} $ .
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