(B) We know that for any two events $A$ and $B$,the addition theorem of probability is given by: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$ Comparing t

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(B) We know that for any two events $A$ and $B$,the addition theorem of probability is given by: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$ Comparing this with the given equation: $P(A \cup B) = a P(A \cap B) + b P(A) + c P(B)$ We get the coefficients as: $a = -1, b = 1, c = 1$ Now,substituting these values into the expression $3a + 2b + 5c$: $3(-1) + 2(1) + 5(1) = -3 + 2 + 5 = 4$ Thus,the value is $4$.

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

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For any two events $A$ and $B$,if $P(A \cup B) = a P(A \cap B) + b P(A) + c P(B)$,then $3a + 2b + 5c = ?$

AP EAMCET 2020 All AP EAMCET

A
$2$
B
$4$
C
$3$
D
$1$

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Probability

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Odds in favor and odds against, Addition theorem on probability

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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) = $

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For an event,the odds against are $6 : 5$. The probability that the event does not occur is

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Fill in the blanks in the following table:

$P(A)$ $P(B)$ $P(A \cap B)$ $P(A \cup B)$

$0.5$ $0.35$ $.........$ $0.7$

Easy

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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 $P(A' \cap B')$.

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$P(A \cup B) = P(A \cap B)$ if and only if the relation between $P(A)$ and $P(B)$ is

DifficultIIT 1985

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$P(A)$	$P(B)$	$P(A \cap B)$	$P(A \cup B)$
$0.5$	$0.35$	$.........$	$0.7$

For any two events $A$ and $B$,if $P(A \cup B) = a P(A \cap B) + b P(A) + c P(B)$,then $3a + 2b + 5c = ?$

Similar Questions

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) = $

For an event,the odds against are $6 : 5$. The probability that the event does not occur is

Fill in the blanks in the following table: $P(A)$ $P(B)$ $P(A \cap B)$ $P(A \cup B)$ $0.5$ $0.35$ $.........$ $0.7$

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

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Fill in the blanks in the following table:

$P(A)$ $P(B)$ $P(A \cap B)$ $P(A \cup B)$

$0.5$ $0.35$ $.........$ $0.7$