The odds against a person who is 40 years old | vedclass

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

Question

(B) Let $A$ be the event that the first person is alive after $30$ years and $B$ be the event that the second person is alive after $30$ years.Given t

Vedclass · Accepted Answer

$\frac{44}{91}$

Vedclass · Answer

(B) Let $A$ be the event that the first person is alive after $30$ years and $B$ be the event that the second person is alive after $30$ years.Given the odds against $A$ are $8:5$,the probability that the first person dies is $P(\bar{A}) = \frac{8}{8+5} = \frac{8}{13}$.Thus,the probability that the first person is alive is $P(A) = 1 - \frac{8}{13} = \frac{5}{13}$.Given the odds against $B$ are $4:3$,the probability that the second person dies is $P(\bar{B}) = \frac{4}{4+3} = \frac{4}{7}$.Thus,the probability that the second person is alive is $P(B) = 1 - \frac{4}{7} = \frac{3}{7}$.The event that exactly one of them is alive is $(\bar{A} \cap B) \cup (A \cap \bar{B})$.Since these events are independent,the probability is $P(\bar{A})P(B) + P(A)P(\bar{B})$.$= (\frac{8}{13} 	imes \frac{3}{7}) + (\frac{5}{13} 	imes \frac{4}{7})$$= \frac{24}{91} + \frac{20}{91} = \frac{44}{91}$.

The odds against a person who is $40$ years old living until he is $70$ are $8$ to $5$,and the odds against another person who is $50$ years old living until he is $80$ are $4$ to $3$. Find the probability that exactly one of them will be alive $30$ years from now.

Similar Questions

If $A$ and $B$ are two independent events,then $P(A \cup B) = $

One card is drawn from a pack of $52$ cards. The probability that it is a king or a diamond is

If $E$ and $F$ are events such that $P(E) = \frac{1}{4}$,$P(F) = \frac{1}{2}$ and $P(E \cap F) = \frac{1}{8}$,find $P(E \cup F)$.

In a horse race,the odds in favour of three horses are $1:2$,$1:3$,and $1:4$. The probability that one of the horses will win the race is

What is the probability of drawing either a queen or a red card from a deck of $52$ cards?

Vedclass Test Series

Exam Paper Generator

Online Exam Module