Independence

Probability Level pending

Let $E$ and $F$ be two independent events . and $E'$ , $F'$ be their complement .

Then

$\large (1)$ Events $E$ and $F'$ are also independent events.

$\large (2)$ Events $E'$ and $F$ are also independent events.

Which of the given options is correct?

Statement

2

is true but Statement

1

is false Statement

1

is true but Statement

2

is false Both the statement

1

and

2

are false Both the statement

1

and

2

are true.

1 solution

Brian Charlesworth
Mar 22, 2017

Since $E$ and $F$ are independent then we know that $P(E \cap F) = P(E) P(F)$ .

Now $P(E \cap F') = P(E) - P(E \cap F) = P(E) - P(E)P(F) = P(E)(1 - P(F)) = P(E)P(F')$ ,

and thus events $E$ and $F'$ are independent. Similarly events $E'$ and $F$ are independent, and so the correct option is $\boxed{\text{Both statements 1 and 2 are true}}$ .

Independence

1 solution

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