A medicine is known to be 75% effective to cure a patient. If the medicine is given to 5 patients, what is the probability that at least one patient is cured by this medicine?

For two events A and B, it is given that $$P(A) = {3 \over {5}}$$ $$P(B) = {3 \over {10}}$$ and $$P(A/B) = {2 \over 3}$$. If $$\overline A $$ and $$\overline B $$ are the complementary events of A and B, then what is $$P(\overline A /\overline B )$$ equal to ?

A machine had three parts, A, B and C, whose chances of being defective are 0.02, 0.10 and 0.05 respectively. The machine stops working if any one of the parts becomes defective. What is the probability that the machine will not stop working?

Three independent events, A₁, A₂ and A₃ occur with probabilities $$P({A_i}) = {1 \over {1 + i}}$$, i = 1, 2, 3. What is the probability that at least one of the three events occurs?