The probability of two students A and B coming to school on time are \frac{2}{7} and \frac{4}{7} ,  respectively. Assuming that the events ‘A coming on time’ and ‘B coming on time’ are independent, find the probability of only one of them coming to school on time.

 

 

 

 
 
 
 
 

Answers (1)

Let E1 : A comimg on time and 
      E2: B coming on time
Here p\left ( E_{1} \right )= \frac{2}{7},\; \; p\left ( \vec{E_{1}} \right )= \frac{5}{7}
        p\left ( E_{2} \right )= \frac{4}{7},\; \; p\left ( \vec{E_{2}} \right )= \frac{3}{7}
\therefore  p(only one on time) = p\left ( E_{1} \right )p\left ( \bar{E_{2}} \right )+p\left ( E_{2} \right )p\left ( \bar{E_{1}} \right )
                                     =\frac{2}{7}\times \frac{3}{7}+\frac{4}{7}\times \frac{5}{7}
                                     =\frac{26}{49}  
         

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