Let 0

Question

(D) Given that $P(A \cup B) = P(A) + P(B) - P(A)P(B)$.We know that the general addition theorem is $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.Comparing

Vedclass · Accepted Answer

Both $(a)$ and $(c)$

Vedclass · Answer

(D) Given that $P(A \cup B) = P(A) + P(B) - P(A)P(B)$.We know that the general addition theorem is $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.Comparing these two,we get $P(A \cap B) = P(A)P(B)$,which implies that events $A$ and $B$ are independent.If $A$ and $B$ are independent,then $P(A/B) = P(A)$,so statement $(a)$ is correct.Also,if $A$ and $B$ are independent,then their complements $A^c$ and $B^c$ are also independent.By De Morgan's Law,$(A \cup B)^c = A^c \cap B^c$.Therefore,$P((A \cup B)^c) = P(A^c \cap B^c) = P(A^c)P(B^c)$ because $A^c$ and $B^c$ are independent. Thus,statement $(c)$ is also correct.Since both $(a)$ and $(c)$ are correct,the final answer is $(d)$.

Let $0 < P(A) < 1$,$0 < P(B) < 1$ and $P(A \cup B) = P(A) + P(B) - P(A)P(B).$ Then

Similar Questions

In a class,$30 \%$ of students passed English,$20 \%$ passed French and $10 \%$ passed both. If a student is selected at random,what is the probability that he has passed English or French?

If two dice are thrown simultaneously,then the probability that $1$ comes on the first die is:

The probability of getting at least one tail in $4$ throws of a coin is

Study the given information carefully and answer the questions that follow: $A$ basket contains $4$ red,$5$ blue and $3$ green marbles. If $2$ marbles are drawn at random,what is the probability that both are red?

$A$ and $B$ toss a coin alternatively,the first to show a head being the winner. If $A$ starts the game,the chance of his winning is

Vedclass Test Series

Exam Paper Generator

Online Exam Module