(B) Given that events $A$ and $B$ are independent,we have $P(A \cap B) = P(A) \times P(B) = 0.4x$.Using the addition theorem of probability: $P(A \cup

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(B) Given that events $A$ and $B$ are independent,we have $P(A \cap B) = P(A) \times P(B) = 0.4x$.Using the addition theorem of probability: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.Substituting the given values: $0.7 = 0.4 + x - 0.4x$.$0.7 - 0.4 = x(1 - 0.4)$.$0.3 = 0.6x$.$x = \frac{0.3}{0.6} = \frac{1}{2}$.

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

Medium

If $P(A) = 0.4$,$P(B) = x$,$P(A \cup B) = 0.7$ and the events $A$ and $B$ are independent,then $x =$

A
$1/3$
B
$1/2$
C
$2/3$
D
None of these

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Odds in favor and odds against, Addition theorem on probability

$A$ die is thrown. Let $A$ be the event that the number obtained is greater than $3$. Let $B$ be the event that the number obtained is less than $5$. Then $P(A \cup B)$ is

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In a horse race,the odds in favour of three horses are $1:2$,$1:3$,and $1:4$. The probability that one of the horses will win the race is

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For two events $A$ and $B$,$P(A)=0.5$,$P(A \cup B)=0.6$ and $P(B)=K$ are given. If $A$ and $B$ are independent events,then $K=$ . . . . . . .

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If $A$ and $B$ are mutually exclusive events,then the value of $P(A \cup B)$ 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 $P(A) = 0.4$,$P(B) = x$,$P(A \cup B) = 0.7$ and the events $A$ and $B$ are independent,then $x =$

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