 The probability that event A occurs is 0,3, the probability that event B does not occur is 0,4. What is the probability that events A and B occur simultaneously if P(A ∪ B) = 0, 7? naivlingr 2021-05-14 Answered
The probability that event A occurs is 0,3, the probability that event B does not occur is 0,4. What is the probability that events A and B occur simultaneously if $$\displaystyle{P}{\left({A}∪{B}\right)}={0},{7}$$?

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Here it is given that he probability that event A occurs is $$P(A)=0.3$$, the probability that event B does not occur is 0.4 that is $$\displaystyle{P}{\left({B}^{{c}}\right)}={0.4}$$ therefore $$\displaystyle{P}{\left({B}\right)}={1}-{P}{\left({B}^{{c}}\right)}={1}-{0.4}={0.6}$$
For two event A and B, we know that $$\displaystyle{P}{\left({A}∪{B}\right)}={P}{\left({A}\right)}+{P}{\left({B}\right)}-{P}{\left({A}⋂{B}\right)}$$.
Now if $$P(A∪B)=0.7$$. therefore

$$\displaystyle{P}{\left({A}⋂{B}\right)}={P}{\left({A}\right)}+{P}{\left({B}\right)}-{P}{\left({A}∪{B}\right)}=0.3+0.6-0.7 =0.9-0.7 =0.2$$
Therefore the probability that events A and B occur simultaneously is 0.02