Question

the odds agains A solving a problem are 10 to 7 and the odd in favour of B solving the problem are 15 to 12 what is the probability that if both of them try.the problem will be solved?
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Answer 1

P(A)= Probability of A solving the problem =  

8+6

6

​

=  

7

3

​

 

P(B)= Probability of B solving the problem =  

14+12

14

​

=  

13

7

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∴   P(A∪B)= Probability of A & B solving the problem independently

                        =P(A)+P(B)−P(A∩B)

                        =P(A)+P(B)−P(A).P(B)        (∵   if A and B are independent)

 

                        =  

7

3

​

+  

13

7

​

−  

13

3

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                                        events then P(A∩B)=P(A).P(B) )

                        =  

91

39+49−21

​

 

                        =  

91

88−21

​

 

                        =  

91

67

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          (Ans.)