The odds against a certain event is 5 : 2 and | vedclass

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(B) Let $A$ and $B$ be two independent events.The odds against $A$ are $5 : 2$,so the probability of $A$ occurring is $P(A) = \frac{2}{5 + 2} = \frac{

Vedclass · Accepted Answer

$\frac{52}{77}$

Vedclass · Answer

(B) Let $A$ and $B$ be two independent events.The odds against $A$ are $5 : 2$,so the probability of $A$ occurring is $P(A) = \frac{2}{5 + 2} = \frac{2}{7}$.Thus,$P(\bar{A}) = 1 - \frac{2}{7} = \frac{5}{7}$.The odds in favour of $B$ are $6 : 5$,so the probability of $B$ occurring is $P(B) = \frac{6}{6 + 5} = \frac{6}{11}$.Thus,$P(\bar{B}) = 1 - \frac{6}{11} = \frac{5}{11}$.The probability that at least one of the events will happen is $P(A \cup B) = 1 - P(\bar{A}) 	imes P(\bar{B})$.$P(A \cup B) = 1 - (\frac{5}{7} 	imes \frac{5}{11}) = 1 - \frac{25}{77} = \frac{77 - 25}{77} = \frac{52}{77}$.

$X$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$
$P(X)$	$0.15$	$0.23$	$0.12$	$0.10$	$0.20$	$0.08$	$0.07$	$0.05$

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

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