A) \[\frac{5}{12}\]
B) \[\frac{5}{6}\]
C) \[\frac{25}{60}\]
D) \[\frac{26}{60}\]
Correct Answer: D
Solution :
Probability that A hits the aim, \[P(\overline{A})=\frac{4}{5}\] Probability that A does not hit the aim, \[P(B)=\frac{3}{4}\] Probability that B hits the aim \[P(B)=\frac{3}{4}\] Probability that B does not hit the aim, \[P(\overline{B})=\frac{1}{4}\] Probability that C hits the aim,\[P(C)=\frac{2}{3}\] Probability that C does not hit the aim\[P(\overline{C})=\frac{1}{3}\] \[\therefore \]Required probability \[=P(A\cap B\cap \overline{C})+(\overline{A}\cap B\cap C)+P(A\cap \overline{B}\cap C)\] \[=P(A)P(B)P(\overline{C})+P(\overline{A})P(B)P(C)+P(A)P(\overline{B})P(C)\] \[=\frac{4}{5}.\frac{3}{4}.\frac{1}{3}+\frac{1}{5}.\frac{3}{4}.\frac{2}{3}+\frac{4}{5}.\frac{1}{4}.\frac{2}{3}\] \[=\frac{12+6+8}{60}=\frac{26}{60}\]
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