(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

If $A$ and $B$ are two events such that $P(A \cup B) + P(A \cap B) = \frac{7}{8}$ and $P(A) = 2P(B)$, then $P(A) = $

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If the probability of a horse $A$ winning a race is $1/4$ and the probability of a horse $B$ winning the same race is $1/5$,then the probability that either of them will win the race is (in $/20$)

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An event has odds in favour $4 : 5$. Then,the probability that the event occurs is:

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Suppose that $A, B, C$ are events such that $P(A) = P(B) = P(C) = \frac{1}{4}$,$P(AB) = P(CB) = 0$,and $P(AC) = \frac{1}{8}$. Then find $P(A \cup B)$.

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If the probability for $A$ to fail in an exam is $0.2$ and that for $B$ is $0.3$,then the probability that either $A$ or $B$ fails is $\leq \ldots \ldots$.

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

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If $A$ and $B$ are two events such that $P(A \cup B) + P(A \cap B) = \frac{7}{8}$ and $P(A) = 2P(B)$, then $P(A) = $

If the probability of a horse $A$ winning a race is $1/4$ and the probability of a horse $B$ winning the same race is $1/5$,then the probability that either of them will win the race is (in $/20$)

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