An experiment has 10 equally likely outcomes. | vedclass

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

Question

(D) Let $n(S) = 10$ be the total number of outcomes. Given $n(A) = 4$,so $P(A) = \frac{4}{10} = \frac{2}{5}$.Let $n(B) = p$,so $P(B) = \frac{p}{10}$.F

Vedclass · Accepted Answer

$5$ or $10$

Vedclass · Answer

(D) Let $n(S) = 10$ be the total number of outcomes. Given $n(A) = 4$,so $P(A) = \frac{4}{10} = \frac{2}{5}$.Let $n(B) = p$,so $P(B) = \frac{p}{10}$.For $A$ and $B$ to be independent,$P(A \cap B) = P(A) 	imes P(B) = \frac{2}{5} 	imes \frac{p}{10} = \frac{2p}{50} = \frac{p}{25}$.Since $P(A \cap B) = \frac{n(A \cap B)}{10}$,we have $\frac{n(A \cap B)}{10} = \frac{p}{25}$,which implies $n(A \cap B) = \frac{10p}{25} = \frac{2p}{5}$.Since $n(A \cap B)$ must be an integer,$2p$ must be divisible by $5$. Since $2$ and $5$ are coprime,$p$ must be a multiple of $5$.Given $B$ is non-empty,$p \in \{5, 10\}$.

An experiment has $10$ equally likely outcomes. Let $A$ and $B$ be two non-empty events of the experiment. If $A$ consists of $4$ outcomes,the number of outcomes that $B$ must have so that $A$ and $B$ are independent,is

Similar Questions

$A$ fair die is rolled. Consider events $E=\{1,3,5\}, F=\{2,3\},$ and $G=\{2,3,4,5\}$. Find $P((E \cup F) | G)$ and $P((E \cap F) | G)$.

If $C$ and $D$ are two events such that $C \subset D$ and $P(D) \neq 0$,then which of the following is true?

If $A$ and $B$ are two events of a random experiment such that $P(A)=0.6$,$P(B)=0.3$,and $P(A \mid B)=0.5$,then $P(\bar{B} \mid \bar{A})=$

Three coins are tossed. If one of them shows tail,then the probability that all three coins show tail,is

If $A$ and $B$ are any two events such that $P(A) = \frac{2}{5}$ and $P(A \cap B) = \frac{3}{20}$,then the conditional probability $P(A | A' \cup B')$,where $A'$ denotes the complement of $A$,is equal to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module