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

Question

The odds against a certain event are 5: 2 and the odds in favour of another independent event are 6: 5 . The probability that at least one of the events will happen, is (A)  (25/77)  (B)  (52/77)  (C)  (12/77)  (D)  (65/77)

Tardigrade Admin · Accepted Answer

Let A and B are two given events. ∴ P(A)=(2/7), P(B)=(6/11) ∴ Required probability =1-P( barA) P( barB) =1-(1-(2/7))(1-(6/11)) =(52/77)

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

$\frac{25}{77}$

$\frac{52}{77}$

$\frac{12}{77}$

$\frac{65}{77}$

Let $A$ and $B$ are two given events.
$∴ P (A) = \frac{2}{7}, P (B) = \frac{6}{11}$
$∴$ Required probability $= 1 - P (\overset{ˉ}{A}) P (\overset{ˉ}{B})$
$= 1 - (1 - \frac{2}{7}) (1 - \frac{6}{11})$
$= \frac{52}{77}$

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

7725​

7752​

7712​

7765​