Question

The odds against a certain event is 5 : 2 and the odds in favour of another event is 6 : 5. If both the events are independent, then the probability that at least one of the events will happen is

• A. $\frac { 50 } { 77 }$
• B. $\frac { 52 } { 77 }$
• C. $\frac { 25 } { 88 }$
• D. $\frac { 63 } { 88 }$

Answer 1

Answer: (B)

$\frac { 52 } { 77 }$

Answer 2

Let $A$ and be two given events. The odds against $A$ are $5 : 2$, therefore $P ( A ) = \frac { 2 } { 7 }$.

The odds in favour of are $6 : 5$, therefore

The required probability $= 1 - P ( \bar { A } ) P ( \bar { B } )$