If A and B are two events, the probability of occurrence of either A or B is given by

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Suppose A and B are two independent events, associated with a random experiment. The probability of occurrence of event A or B is 0.8, while the probability of occurrence of event A is 0.5.Determine the occurrence of the probability of Event B.

I have searched a lot for this question. I am new to probability. How can we convert the basic formulae for this?

P(A)+P(B)-P(A intersection B)= P(A union B)

Thanks for the help in advance. Please down mark this question as after this my account will get blocked

Answer

Hint: In probability theory, Events \[{{\text{E}}_1},{{\text{E}}_2},\_\_\_\]En are said to be mutually exclusive if the occurrence of them implies the non-occurrence of the remaining (n-1) events. Therefore, two mutually exclusive events cannot both occur and formally said the intersection of each two of them is empty (the null events). In consequence mutually exclusive events have the property:\[{\text{P(A}} \cap {\text{B) = E}}\]

Complete step-by-step answer:

Hence option B is correct.

Note: In logic two mutually exclusive prepositions that logically cannot be true in the same sense at the same time. To say that more than two propositions are mutually exclusive, depending on context, means that one cannot be true if the other one is true or at least one of them cannot be true.