A) \[1/8\]
B) \[1/4\]
C) \[1/2\]
D) \[2/3\]
Correct Answer: B
Solution :
Let \[{{A}_{1}},{{A}_{2}}\] and \[{{A}_{3}}\] be the events of match winning in first, second and third match respectively and whose probabilities are \[P({{A}_{1}})=P({{A}_{2}})=P({{A}_{3}})=\frac{1}{2}\] Required probability \[=P({{A}_{1}}\,A{{'}_{2}}{{A}_{3}})+P(A_{1}^{'}\,{{A}_{2}}\,{{A}_{3}})\] \[=P({{A}_{1}})P({{A}_{2}}')P({{A}_{3}})+P({{A}_{1}}')P({{A}_{2}})P({{A}_{3}})\] \[={{\left( \frac{1}{2} \right)}^{3}}+{{\left( \frac{1}{2} \right)}^{3}}=\frac{1}{8}+\frac{1}{8}=\frac{1}{4}\]You need to login to perform this action.
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