The probabilities of solving a specific problem independently by A and B are \frac{1}{3}\; and\; \frac{1}{5}  respectively. If both try to solve the problem independently,find the probability that the problem is solved.

 

 

 

 
 
 
 
 

Answers (1)

Let A: A solves the problem and B:B solves the problem independently.
given that p\left ( A \right )= \frac{1}{3}\;\; \; p\left ( B \right )= \frac{1}{5}
\therefore p\left ( \bar{A} \right )=1-p\left ( A \right )= \frac{2}{3}\: ,p\left ( \bar{B} \right )= \frac{4}{5}
\therefore  p(the problem is solved)= 1-p (the problem is not solved)
                                           = 1-p\left ( \bar{A} \right )p\left ( \bar{B} \right )
                                          \Rightarrow 1-\frac{2}{3}\times \frac{4}{5}= \frac{7}{15}
Alternatively, we p(the problem is solved)
                    = p\left ( A \right )p\left ( B \right )+p\left ( \bar{A} \right )p\left ( B \right )+p\left ( \bar{B} \right )p\left ( A \right )

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