(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

One card is drawn randomly from a pack of $52$ cards. The probability that it is a king or a spade is:

Medium

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Given two independent events $A$ and $B$ such that $P(A) = 0.3$ and $P(B) = 0.6$. Find $P(\text{neither } A \text{ nor } B)$.

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In class $XI$ of a school,$40\%$ of the students study Mathematics and $30\%$ study Biology. $10\%$ of the class study both Mathematics and Biology. If a student is selected at random from the class,find the probability that they will be studying Mathematics or Biology.

Easy

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The probability that $A$ speaks the truth is $\frac{4}{5}$,while the probability that $B$ speaks the truth is $\frac{3}{4}$. What is the probability that they contradict each other when asked to speak on a fact?

MediumAIEEE 2004

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There are three events $A, B, C$,one of which must and only one can happen. The odds are $8:3$ against $A$,$5:2$ against $B$,and the odds against $C$ are $43:17k$. Then the value of $k$ is:

DifficultMHT CET 2024

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

Similar Questions

One card is drawn randomly from a pack of $52$ cards. The probability that it is a king or a spade is:

Given two independent events $A$ and $B$ such that $P(A) = 0.3$ and $P(B) = 0.6$. Find $P(\text{neither } A \text{ nor } B)$.

In class $XI$ of a school,$40\%$ of the students study Mathematics and $30\%$ study Biology. $10\%$ of the class study both Mathematics and Biology. If a student is selected at random from the class,find the probability that they will be studying Mathematics or Biology.

The probability that $A$ speaks the truth is $\frac{4}{5}$,while the probability that $B$ speaks the truth is $\frac{3}{4}$. What is the probability that they contradict each other when asked to speak on a fact?

There are three events $A, B, C$,one of which must and only one can happen. The odds are $8:3$ against $A$,$5:2$ against $B$,and the odds against $C$ are $43:17k$. Then the value of $k$ is:

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