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

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

Vedclass · Accepted Answer

$\frac{52}{77}$

Vedclass · Answer

(B) Let $A$ and $B$ be two independent events. The odds against event $A$ are $5:2$,so the probability of $A$ occurring is $P(A) = \frac{2}{5+2} = \frac{2}{7}$. The probability of $A$ not occurring is $P(\bar{A}) = 1 - \frac{2}{7} = \frac{5}{7}$. The odds in favour of event $B$ are $6:5$,so the probability of $B$ occurring is $P(B) = \frac{6}{6+5} = \frac{6}{11}$. The probability of $B$ not occurring is $P(\bar{B}) = 1 - \frac{6}{11} = \frac{5}{11}$. Since the events are independent,the probability that at least one event happens is $P(A \cup B) = 1 - P(\bar{A} \cap \bar{B}) = 1 - P(\bar{A})P(\bar{B})$. $P(A \cup B) = 1 - (\frac{5}{7} 	imes \frac{5}{11}) = 1 - \frac{25}{77} = \frac{77-25}{77} = \frac{52}{77}$.

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

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