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JEE Advanced 2007Paper 2

Exam: JEE Advanced
Year: 2007
Paper: Paper 2
Subject: Mathematics
Chapter: Probability

JEE Advanced 2007 · Paper 2 · Mathematics · Probability

Let E^c denotes the complement of an event E . Let E, F, G be...

Let

E^c

denotes the complement of an event

E

. Let

E, F, G

be pairwise independent events with

P(G)>0 and

P(E \cap F \cap G)=0

. Then,

P\left(E^c \cap F^c \mid G\right)

equals

Options

A $P\left(E^c\right)+P\left(F^c\right)$
B $P\left(E^c\right)-P\left(F^c\right)$
C $P\left(E^c\right)-P(F)$
D $P(E)-P\left(F^c\right)$

Correct answer

C. $P\left(E^c\right)-P(F)$

Step-by-step solution

\begin{aligned}P\left(\frac{E^c \cap F^c}{G}\right)& =\frac{P\left(E^c \cap F^c \cap G\right)}{P(G)}\\ & =\frac{P(G)-P(E \cap G)-P(G \cap F)}{P(G)}\\ & =\frac{P(G)[1-P(E)-P(F)]}{P(G)}\\ & =1-P(E)-P(F) \\ & =P \left(E^c\right)-P(F) . \end{aligned}

$

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