Probability

Total number of fruits in one basket $=5$ apples +7 oranges $=12$Probability of picking an apple from Ist basket $=\;\frac{5}{12}=P (A_1)$ Probability of picking an orange from Ist basket $=\;\frac{7}{12}=P (B_1)$ Total number of fruits in second baskd=4 apples +8 oranges $=12$ Probability of picking an apples from IInd basket, $P (A_2) =\;\frac{4}{12}$Probability of picking an oranges from IInd basket $P (B_2) =\;\frac{8}{12}$Probability of picking an apple from Ist and an orange from IInd basket$=\;\frac{5}{12} \times \;\frac{8}{12} = \;\frac{40}{144} = \;\frac{10}{36} = \;\frac{5}{18}$Probability of picking an apple from IInd basket and an orange from Ist basket $=\;\frac{4}{12} \times \;\frac{7}{12} = \;\frac{28}{144}$So, total probability$=\;\frac{40}{144} + \;\frac{28}{144} = \;\frac{68}{144} = \;\frac{17}{36}$