​ If E and F are events such that P(E) = 1/4, P(F) = 1/2 and P(E and F) =1/8 . Find 1. P(E or F) 2. P(not E and not F) ​

Question

If E and F are events such that P(E) = \(\frac{1}{4}\), P(F) = \(\frac{1}{2}\) and P(E and F) = \(\frac{1}{8}\). Find

1. P(E or F)

2. P(not E and not F)

Answer 1

P(E) = \(\frac{1}{4}\), P(F) = \(\frac{1}{2}\); P(E ∩ F) = \(\frac{1}{8}\)

1. P(E ∪ F) = P(E) + P(F) – P(E ∩ F)

\(\frac{1}{4} + \frac{1}{2} - \frac{1}{8} = \frac{5}{8}\)

2. P(not E and not F) = P(E’ ∩ F’) = P(E ∪ F)’

= 1 – P(E ∪ F) = 1 – \(\frac{5}{8}\) = \(\frac{3}{8}\)