Question

What is the probability of the union of the complement of event E (denoted as E_c) and the complement of event F (denoted as F_c), given that P(E)=0.35,P(E)=0.35, P(F)=0.67, and P(Ec∪F)=0.86?

Answer 1

The probability of the union of the complement of event E (E_c) and the complement of event F (F_c) is 0.86.

Step-by-step explanation:

The question asks to find the probability of the union of the complement of event E (E_c) and the complement of event F (F_c), given P(E) = 0.35, P(F)= 0.67, and P(Ec ∪ F) = 0.86.

To find this probability, we need to use the formula P(Ec ∪ Fc) = 1 - P(E ∪ F), and we know that P(E ∪ F) is the complement of P(Ec ∪ F), which is given as 0.86.
To calculate P(E ∪ F), we start by understanding that P(E ∪ F) is the complement of P(Ec ∪ F), thus P(E ∪ F) = 1 - P(Ec ∪ F) = 1 - 0.86 = 0.14.

Now, to find P(Ec ∪ Fc), we use the formula for the complement of the union of two events, which is: P(Ec ∪ Fc) = 1 - P(E ∪ F) = 1 - 0.14 = 0.86. Therefore, the probability of the union of the complements Ec and Fc is 0.86.