Question

The odds in favour of an event is 2:3 and the odds against the another event event is 3:7.Then find the probability that one of the ev

Answer 1

Please see the attachment

Answer 2

Given :

The odds in favour of event = 2 : 3

The odds against of another event = 3 : 7

To Find :

The probability that one of the event

Solution :

As , Odds in favour of event = P ( $E_1$ ) = 2 : 5 = $\dfrac{2}{5}$

So, Odds against of event =  P ( $E_1$' ) = 1 - $\dfrac{2}{5}$  

                                                             = $\dfrac{3}{5}$

Again

odds against of another event =  P ( $E_2$' ) = 3 : 10  = $\dfrac{3}{10}$

So,   Odds in favour of event = P ( $E_2$  ) = 1 - $\dfrac{3}{10}$

                                                              = $\dfrac{7}{10}$

Now

The probability that one of the event = P [ ( $E_1$ $(\cap )$ $E_2$' )   U (

                                                             = P ( $E_1$ ) . P ( $E_2$' ) +  P (

                                                             = $\dfrac{2}{5}$  ×  $\dfrac{3}{10}$   +   $\dfrac{3}{5}$  × $\dfrac{7}{10}$

                                                             = $\dfrac{6}{50}$  +  $\dfrac{21}{50}$

                                                             = $\dfrac{27}{50}$

Hence, The probability that one of the event is $\dfrac{27}{50}$  . Answer