If the events A and B are mutually exclusive events such that P ( A ) = 3 3 x + 1 and P ( B ) = 4 1 − x , then the set of possible values of x lies in the interval :

Since events A and B are mutually exclusive ∴ P ( A ) + P ( B ) = 1 ⇒ 3 3 x + 1 + 4 1 − x = 1 ⇒ 12 x + 4 + 3 − 3 x = 12 ⇒ 9 x = 5 ⇒ x = 9 5 ∴ x ∈ [ − 3 1 , 9 5 ]

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MathematicsProbabilityIndependent eventsMedium2 minPYQ_2013

MathematicsMediumsingle choice

If the events $A$ and $B$ are mutually exclusive events such that $P (A) = \frac{3 x + 1}{3}$ and $P (B) = \frac{1 - x}{4}$ , then the set of possible values of $x$ lies in the interval :

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Answer:

Solution:

Since events A and B are mutually exclusive $∴ P (A) + P (B) = 1 \Rightarrow \frac{3 x + 1}{3} + \frac{1 - x}{4} = 1 \Rightarrow 12 x + 4 + 3 - 3 x = 12 \Rightarrow 9 x = 5 \Rightarrow x = \frac{5}{9} ∴ x \in [- \frac{1}{3}, \frac{5}{9}]$

Stream:JEESubject:MathematicsTopic:ProbabilitySubtopic:Independent events

⏱ 2mℹ️ Source: PYQ_2013

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