Question

For an event E, P(E) + P(E') = q, then

(a) 0 ≤ q < 1

(b) 0 < q ≤ 1

(c) 0 < q < 1

(d) none of these​

Answer 1

Answer:

The correct answer is 'a'.

Step by step explanation:

p(e) + p(not e) = 1

p(not e) = 1- p(e)

So p(not e) will always be lesser than 1 . Not equal to 1.

So it can be either equal to or greater than 0 and lesser than 1.

Answer 2

For an event E, P(E) + P(E') = q, then (b) 0 <  q ≤ 1.

• We know that the maximum value of a probability is always 1.

• From above, the event is given as E, and P(E) is the probability of that event that will occur or termed as the probability of success and P(E') is the probability of that event that will not occur or be termed as the probability of failure and it is the complement of P(E).

• Let us assume that the probability of success P(E) is 0, then the probability of failure P(E') will be 1 as it is the complement of P(E), so

                 ∴ P(E) + P(E')=0+1=1  [and we know the maximum value of any

                                                             probability is always 1]