Question

If E and F are disjoint​ events, then P(E or F) equals __________.

a. P(E) + P(F) - P(E and F).
b. P(E) + P(F).
c. P(F).
d. P(E).
e. P(E and F).

Answer 1

b) P(E or F) = P(E) + P(F)

Explanation:

Here, given:

E and F are disjoint events.

Any two events are said to be disjoint if they cannot occur simultaneously.

For Example: Getting a head and a tail if a fair coin is flipped.

Now, we need to find P( E or F)

Now, as E and F are mutually disjoint.

⇒ P (E ∩ F ) = Ф

Also, we know : P(E or F) = P(E U F) = P(E) + P(F) - P (E ∩ F )

⇒ P(E or F) = P(E) + P(F)