Let $X$ and $Y$ be two events of a sample space such that $P(X)=\frac{1}{3}$, $P(X|Y)=\frac{1}{2}$ and $P(Y|X)=\frac{2}{5}$, then which of the following is true?
- A$P(X \cap Y)=\frac{1}{5}$
- B$P(X \cup Y)=\frac{2}{5}$
- C$P(Y)=\frac{4}{15}$
- D$P(X \cup Y)=\frac{1}{2}$
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Let $A, B$ and $C$ be three events,which are pairwise independent and $\overline{E}$ denote the complement of an event $E$. If $P(A \cap B \cap C) = 0$ and $P(C) > 0$,then $P((\overline{A} \cap \overline{B}) / C)$ is equal to
$A$ coin is tossed three times in succession. If $E$ is the event that there are at least two heads and $F$ is the event in which the first throw is a head,then $P(E|F) = $
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View SolutionLet $A$ and $B$ be two events such that $P(B \mid A) = \frac{2}{5}$,$P(A \mid B) = \frac{1}{7}$ and $P(A \cap B) = \frac{1}{9}$. Consider:
$(S1) P(A' \cup B) = \frac{5}{6}$
$(S2) P(A' \cap B') = \frac{1}{18}$.
Then:
$(S1) P(A' \cup B) = \frac{5}{6}$
$(S2) P(A' \cap B') = \frac{1}{18}$.
Then:
DifficultJEE MAIN 2022
View SolutionIn a school,there are $1000$ students,out of which $430$ are girls. It is known that out of $430$,$10\%$ of the girls study in class $XII$. What is the probability that a student chosen randomly studies in class $XII$ given that the chosen student is a girl?
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