If {A₁},,{A₂},...{Aₙ} are any n events, then

English

Gujarati

Hindi

14.Probability

normal

If ${A_1},\,{A_2},...{A_n}$ are any $n$ events, then

$P\,({A_1} \cup {A_2} \cup ... \cup {A_n}) = P\,({A_1}) + P({A_2}) + ... + P\,({A_n})$

$P\,({A_1} \cup {A_2} \cup ... \cup {A_n}) > P\,({A_1}) + P({A_2}) + ... + P\,({A_n})$

$P\,({A_1} \cup {A_2} \cup ... \cup {A_n}) \le P\,({A_1}) + P({A_2}) + ... + P\,({A_n})$

None of these

Solution

$P(A \cup B) = P(A) + P(B) – P(A \cap B)$

$\therefore \,\,\,P(A \cup B) \le P(A) + P(B).$

Using principle of mathematical induction, it can be easily established that $P\left( {\mathop \cup \limits_{i = 1}^n {A_i}} \right) \le \sum\limits_{i = 1}^n {P({A_i}).} $

Standard 11

Mathematics

Two students Anil and Ashima appeared in an examination. The probability that Anil will qualify the examination is $0.05$ and that Ashima will qualify the examination is $0.10 .$ The probability that both will qualify the examination is $0.02 .$ Find the probability that Atleast one of them will not qualify the examination.

easy

If $A$ and $B$ are two events of a random experiment, $P\,(A) = 0.25$, $P\,(B) = 0.5$ and $P\,(A \cap B) = 0.15,$ then $P\,(A \cap \bar B) = $

easy

If $A$ and $B$ are two events such that $P(A) = 0.4$ , $P\,(A + B) = 0.7$ and $P\,(AB) = 0.2,$ then $P\,(B) = $

easy

Four persons can hit a target correctly with probabilities $\frac{1}{2},\frac{1}{3},\frac{1}{4}$ and $\frac {1}{8}$ respectively. If all hit at the target independently, then the probability that the target would be hit, is

hard

(JEE MAIN-2019)

A party of $23$ persons take their seats at a round table. The odds against two persons sitting together are

easy

If ${A_1},\,{A_2},...{A_n}$ are any $n$ events, then

Solution

Similar Questions

If $A$ and $B$ are two events of a random experiment, $P\,(A) = 0.25$, $P\,(B) = 0.5$ and $P\,(A \cap B) = 0.15,$ then $P\,(A \cap \bar B) = $

If $A$ and $B$ are two events such that $P(A) = 0.4$ , $P\,(A + B) = 0.7$ and $P\,(AB) = 0.2,$ then $P\,(B) = $

Four persons can hit a target correctly with probabilities $\frac{1}{2},\frac{1}{3},\frac{1}{4}$ and $\frac {1}{8}$ respectively. If all hit at the target independently, then the probability that the target would be hit, is

A party of $23$ persons take their seats at a round table. The odds against two persons sitting together are

Start a Free Trial Now