A) \[\frac{31}{56}\]
B) \[\frac{24}{56}\]
C) \[\frac{25}{56}\]
D) None of these
Correct Answer: C
Solution :
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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