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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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 $P(A \cup B) = 1 - P(\bar{A}) 	imes P(\bar{B})$.$P(A \cup B) = 1 - (\frac{5}{7} 	imes \frac{5}{11}) = 1 - \frac{25}{77} = \frac{77 - 25}{77} = \frac{52}{77}$.

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

Similar Questions

$A$ party of $23$ persons take their seats at a round table. The odds against two specific persons sitting together are

If two events $E_1$ and $E_2$ are such that $P(E_1 \cup E_2) = \frac{5}{8}$,$P(\bar{E}_1) = \frac{3}{4}$,and $P(E_2) = \frac{1}{2}$,then $E_1$ and $E_2$ are:

If the probability of $A$ failing an exam is $1/5$ and the probability of $B$ failing is $3/10$,what is the probability that either $A$ or $B$ fails?

If a card is drawn at random from a pack of $52$ cards,the probability that the card is a king or a diamond is $..........$.

The odds in favour of getting a sum that is a multiple of $3$,when a pair of dice is thrown,is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module