Question

The probability that at least one of the two events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.3, evaluate ${\displaystyle \text{P}\left(\overline{\text{A}}\right)+\text{P}\left(\overline{\text{B}}\right)}$

Answer 1

We know that,

A ∪ B denotes that atleast one of the events occurs

And A ∩ B denotes that the two events occur simultaneously.

So, P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

⇒ 0.6 = P(A) + P(B) – 0.3

⇒ 0.9 = P(A) + P(B)

⇒ 0.9 = ${\displaystyle 1-\text{P}\left(\overline{\text{A}}\right)+1-\text{P}\left(\overline{\text{B}}\right)}$

⇒ ${\displaystyle \text{P}\left(\overline{\text{A}}\right)+\text{P}\left(\overline{\text{B}}\right)}$ = 2 – 0.9 = 1.1

Hence, the required answer is 1.1