Question

For an event E, if `P(E) + P(barE)` = q, then the value of q² − 4 is ______.

Options

• −3

• 3

• 5

• −5

Answer 1

For an event E, if `P(E) + P(barE)` = q, then the value of q² − 4 is −3.

Explanation:

In probability theory, the sum of the probability of an event (E) and its complement `p(barE)` is always equal to 1. This is because these two events are exhaustive (cover all possibilities) and mutually exclusive (can't happen together).

So, we know:

`P(E) + P(barE)` = 1

We are given that `P(E) + P(barE)` = q, which must also be equal to 1.

Therefore, q = 1.

Now we can find q² − 4:

q² − 4

= 1² − 4

= 1 − 4

= −3

So the value of q² − 4 is −3.