(A) Let $A$ be the event that a flight departs on time and $B$ be the event that a flight arrives on time. Given probabilities are: $P(A) = 80 \% = 0.

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(A) Let $A$ be the event that a flight departs on time and $B$ be the event that a flight arrives on time. Given probabilities are: $P(A) = 80 \% = 0.80$ $P(B) = 70 \% = 0.70$ $P(A \cap B) = 65 \% = 0.65$ We need to find the conditional probability that a flight arrives on time given that it has departed on time, which is $P(B|A)$. Using the formula for conditional probability: $P(B|A) = \frac{P(A \cap B)}{P(A)}$ Substituting the values: $P(B|A) = \frac{0.65}{0.80} = \frac{65}{80} = \frac{13}{16}$ Thus, the probability is $\frac{13}{16}$.

Class 12 Mathematics Probability Conditional probability

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If $80 \%$ of flights depart on time, $70 \%$ of flights arrive on time and $65 \%$ of flights depart on time and arrive on time, then the probability that a flight that has just departed on time will arrive on time is

TS EAMCET 2019 All TS EAMCET

A
$\frac{13}{16}$
B
$\frac{11}{16}$
C
$\frac{13}{14}$
D
$\frac{11}{14}$

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Probability

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Conditional probability

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TS EAMCET 2019 Paper All TS EAMCET years →

One card is drawn at random from a well-shuffled deck of $52$ cards. In which of the following cases are the events $E$ and $F$ independent?
$E:$ 'the card drawn is black'
$F:$ 'the card drawn is a king'

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If $A$ and $B$ are two events such that $P(A | B) = 0.6$, $P(B | A) = 0.3$, and $P(A) = 0.1$, then $P(\bar{A} \cap \bar{B})$ equals:

EasyTS EAMCET 2015

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If $E_1$ and $E_2$ are two events of a random experiment such that $P(E_1) = \frac{1}{8}$,$P(E_1 \mid E_2) = \frac{1}{3}$,and $P(E_2 \mid E_1) = \frac{1}{4}$,then match the items of List-$I$ with the items of List-$II$.
List-$I$ List-$II$
$A. P(E_1 \cup E_2)$ $I. \frac{3}{29}$
$B. P(E_2)$ $II. \frac{26}{29}$
$C. P(E_1 \mid \bar{E}_2)$ $III. \frac{3}{16}$
$D. P(\bar{E}_1 \mid \bar{E}_2)$ $IV. \frac{3}{32}$

DifficultAP EAMCET 2019

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Given that $A$ and $B$ are two events such that $P(B) = \frac{3}{5}$,$P\left(\frac{A}{B}\right) = \frac{1}{2}$,and $P(A \cup B) = \frac{4}{5}$,then $P(A)$ is equal to:

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In a group of $14$ males and $6$ females, $8$ males and $3$ females are aged above $40 \text{ yr}$. The probability that a person selected at random from the group is aged above $40 \text{ yr}$, given that the selected person is a female, is:

MediumWBJEE 2016

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List-$I$	List-$II$
$A. P(E_1 \cup E_2)$	$I. \frac{3}{29}$
$B. P(E_2)$	$II. \frac{26}{29}$
$C. P(E_1 \mid \bar{E}_2)$	$III. \frac{3}{16}$
$D. P(\bar{E}_1 \mid \bar{E}_2)$	$IV. \frac{3}{32}$

If $80 \%$ of flights depart on time, $70 \%$ of flights arrive on time and $65 \%$ of flights depart on time and arrive on time, then the probability that a flight that has just departed on time will arrive on time is

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One card is drawn at random from a well-shuffled deck of $52$ cards. In which of the following cases are the events $E$ and $F$ independent?$E:$ 'the card drawn is black'$F:$ 'the card drawn is a king'

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One card is drawn at random from a well-shuffled deck of $52$ cards. In which of the following cases are the events $E$ and $F$ independent?
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$F:$ 'the card drawn is a king'