Question

In: Statistics and Probability

Let E and F be independent events. Show that the events E and F care also...

Let E and F be independent events. Show that the events E and F care also independent.

Hint: Start with P(E∩Fc) =P(E)−P(E∩F) and use the independence of E and F.

Expert Solution

We have given

Event E and Event F are independent

According to condition for Independent

That means we have to prove

We know formula

We apply formula for P ( E ∩ F )

So we get

We factor out P (E) from the right side of equation

We know Complement rule of probabiltiy

So we get

So we apply formula of complement rule for [1 - P (F)] In equation becomes

Hence proved.

Final answer :-

From above we can say event E and event are Independent

( Note : Means Complement of Event F the exponent letter " C" means complement , ∩ means intersection sign I.e " AND " sign )

orchestra answered 1 year ago

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