(C) Given that, $P(E) = 1/5$ and $P(F|E) = 1/10$. We know that the probability of both events occurring is given by $P(E \cap F) = P(E) \cdot P(F|E)$.

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(C) Given that, $P(E) = 1/5$ and $P(F|E) = 1/10$. We know that the probability of both events occurring is given by $P(E \cap F) = P(E) \cdot P(F|E)$. Substituting the values, we get $P(E \cap F) = (1/5) \cdot (1/10) = 1/50$. The probability of non-occurrence of at least one of the events $E$ and $F$ is equivalent to the complement of the event that both $E$ and $F$ occur. Thus, the required probability is $1 - P(E \cap F)$. Calculating this, we get $1 - 1/50 = 49/50$.

Class 12 Mathematics Probability Conditional probability

Medium

Suppose $E$ and $F$ are two events of a random experiment. If the probability of occurrence of $E$ is $1/5$ and the probability of occurrence of $F$ given $E$ is $1/10$, then the probability of non-occurrence of at least one of the events $E$ and $F$ is

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A
$1/18$
B
$1/2$
C
$49/50$
D
$1/50$

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Probability

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Conditional probability

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$A$ pair of dice is thrown. If $5$ appears on at least one of the dice,then the probability that the sum is $10$ or greater is:

Easy

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Statement $- I :$ If $A$ and $B$ are two independent events such that $P(A) = 1/2$ and $P(B) = 1/5$,then $P(A|B) = 1/2$.
Statement $- II : P(A|B) = P(A)$ if $A$ and $B$ are independent events.

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If $A$ and $B$ are mutually exclusive events with $P(B) \neq 1$, then $P(A \mid \bar{B})$ is equal to (Here $\bar{B}$ is the complement of the event $B$)

EasyTS EAMCET 2007

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If $A$ and $B$ are two independent events such that $P(A \cap B') = \frac{3}{25}$ and $P(A' \cap B) = \frac{8}{25}$,then $P(A) = $

MediumIIT 2002

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In a hostel,$60 \%$ of the students read Hindi newspaper,$40 \%$ read English newspaper and $20 \%$ read both Hindi and English newspapers. $A$ student is selected at random. If she reads Hindi newspaper,find the probability that she reads English newspaper.

Easy

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Suppose $E$ and $F$ are two events of a random experiment. If the probability of occurrence of $E$ is $1/5$ and the probability of occurrence of $F$ given $E$ is $1/10$, then the probability of non-occurrence of at least one of the events $E$ and $F$ is

Similar Questions

$A$ pair of dice is thrown. If $5$ appears on at least one of the dice,then the probability that the sum is $10$ or greater is:

Statement $- I :$ If $A$ and $B$ are two independent events such that $P(A) = 1/2$ and $P(B) = 1/5$,then $P(A|B) = 1/2$.Statement $- II : P(A|B) = P(A)$ if $A$ and $B$ are independent events.

If $A$ and $B$ are mutually exclusive events with $P(B) \neq 1$, then $P(A \mid \bar{B})$ is equal to (Here $\bar{B}$ is the complement of the event $B$)

If $A$ and $B$ are two independent events such that $P(A \cap B') = \frac{3}{25}$ and $P(A' \cap B) = \frac{8}{25}$,then $P(A) = $

In a hostel,$60 \%$ of the students read Hindi newspaper,$40 \%$ read English newspaper and $20 \%$ read both Hindi and English newspapers. $A$ student is selected at random. If she reads Hindi newspaper,find the probability that she reads English newspaper.

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Statement $- I :$ If $A$ and $B$ are two independent events such that $P(A) = 1/2$ and $P(B) = 1/5$,then $P(A|B) = 1/2$.
Statement $- II : P(A|B) = P(A)$ if $A$ and $B$ are independent events.