(C) For any two events $A$ and $B$,we have the addition theorem of probability:$P(A \cup B) = P(A) + P(B) - P(A \cap B)$Since $P(A \cap B) \ge 0$,it f

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

(C) For any two events $A$ and $B$,we have the addition theorem of probability:$P(A \cup B) = P(A) + P(B) - P(A \cap B)$Since $P(A \cap B) \ge 0$,it follows that $P(A \cup B) \le P(A) + P(B)$.By the principle of mathematical induction,this inequality can be generalized for $n$ events as:$P\left( \bigcup_{i=1}^{n} A_i \right) \le \sum_{i=1}^{n} P(A_i)$.

Class 11 Mathematics Probability Odds in favor and odds against, Addition theorem on probability

Medium

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

A
$P({A_1} \cup {A_2} \cup ... \cup {A_n}) = P({A_1}) + P({A_2}) + ... + P({A_n})$
B
$P({A_1} \cup {A_2} \cup ... \cup {A_n}) > P({A_1}) + P({A_2}) + ... + P({A_n})$
C
$P({A_1} \cup {A_2} \cup ... \cup {A_n}) \le P({A_1}) + P({A_2}) + ... + P({A_n})$
D
None of these

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Odds in favor and odds against, Addition theorem on probability

Let $A$ and $B$ be two events such that $P(A) = 0.3$ and $P(A \cup B) = 0.8$. If $A$ and $B$ are independent events,then $P(B) = $

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The probability that a man will be alive in $20$ years is $\frac{3}{5}$ and the probability that his wife will be alive in $20$ years is $\frac{2}{3}$. Then the probability that at least one will be alive in $20$ years is:

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Three ships $A$, $B$, and $C$ sail from England to India. If the odds in favour of their safe arrival are $2:5$, $3:7$, and $6:11$ respectively, then the probability that exactly two ships arrive safely is

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$A$ and $B$ are two events such that $P(A)=0.54$,$P(B)=0.69$ and $P(A \cap B)=0.35$. Find $P(A \cup B)$.

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

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Let $A$ and $B$ be two events such that $P(A) = 0.3$ and $P(A \cup B) = 0.8$. If $A$ and $B$ are independent events,then $P(B) = $

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