Question

If p(e) = 3/5
P(f) = 3/10 and p(e n f) = 1/5

Are e and f are independent.

Answer 1

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Hey there!

Solution:

If two events are independent they must equal to ; given by:


P(E n F) = P(E).P(F)

Now Acc to question, using values of P(E).P(F)


1/5 = 3/5 × 3/10


1/5 = 9/50

Which is not equal.


So The given question is not independent.




#Be Brainly.

Answer 2

Hey there !

Solution:

Two events X and Y are said to be independent when,

P ( X ∩ Y ) = P ( X ) . P ( Y )

So let us verify it in this sum.

P ( E ∩  F ) = 1 / 5

P ( E ) = 3 / 5 and P ( F ) = 3 / 10

=> P ( E ) . P ( F ) = 3 / 5 * 3 / 10

=> P ( E ) = P ( F ) = 9 / 50

9 / 50 ≠ 1 / 5

=> P ( E ∩ F ) ≠ P ( E ) . P ( F )

Hence E and F are not independent events.

Hope my answer helped !