The odds against an event is 4:5 and the odds in favour of another event is 3:7. If both events are independent, Then the probability that atleast one of the event will happen is

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5/6

31/45

77/90

1/6

answer is A.

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Detailed Solution

$\begin{array}{l} \begin{array}{l} P (\bar{A}) : P (A) = 4 : 5 \to P (A) = 5 / 9 \\ P (B) : P (\bar{B}) = 3 : 7 \to P (B) = 3 / 10 \end{array} \\ P (A \cup B) = P (A) + P (B) - P (A) . P (B) = 31 / 45 \end{array}$

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