The-probability-that-at-least-one-of-the-events-A-and-B-occurs-is-0-7-and-they-occur-simultaneously-with-probability-0-2-Then-P-A-P-B-

Question Number 110826 by Aina Samuel Temidayo last updated on 30/Aug/20

The probability that at least one of

the events A and B occurs is 0.7 and

they occur simultaneously with

probability 0.2 . Then P (\bar{A}) + P (\bar{B}) =

Commented by kaivan.ahmadi last updated on 30/Aug/20

p (A \cup B) = 0.7

p (A \cap B) = 0.2

p (A \cup B) = p (A) + p (B) - p (A \cap B) \Rightarrow

0.7 = p (A) + p (B) - 0.2 \Rightarrow

p (A) + p (B) = 0.9

(1 - p (A)) + (1 - p (B)) = - 0.9 + 2

\Rightarrow p (\bar{A}) + p (\bar{B}) = 1.1

Commented by Aina Samuel Temidayo last updated on 30/Aug/20

Thanks but the question asks us to find

P (\bar{A}) + P (\bar{B}) .

Commented by Aina Samuel Temidayo last updated on 31/Aug/20

Yes .

Commented by Aina Samuel Temidayo last updated on 31/Aug/20

It is a sum . So I think it is accepted .

Commented by kaivan.ahmadi last updated on 31/Aug/20

0 ⩽ p (\bar{A}) ⩽ 1

0 ⩽ p (\bar{B}) ⩽ 1

0 ⩽ p (\bar{A}) + p (\bar{B}) ⩽ 2

Commented by Her_Majesty last updated on 31/Aug/20

P (\bar{A}) + P (\bar{B}) \neq P (\bar{A} \land \bar{B})

t h e s u m o f 2 i n d e p e n d e n t p r o b a b i l i t i e s i s

a s e n s e l e s s v a l u e .

i . e . t h e p r o b a b i l i t y o f a t h r o w n d i c e s h o w i n g

n o t 6 i s \frac{5}{6}, t h e o n e o f a t h r o w n c o i n s h o w i n g

h e a d i s \frac{1}{2} \Rightarrow t h e s u m i s \frac{4}{3} \approx 133 %