Probability Tes...

Given that $$A, B$$ and $$C$$ are events such that $$P(A)=P(B)=P(C)=1/5, P(A\cap B)=P(B\cap C)=0$$ and $$P(A\cap C)=1/10$$. The probability that at least one of the events $$A, B$$ or $$C$$ occurs is

For the three events $$A, B$$ and $$C, P$$ (exactly one of the events $$A$$ or $$B$$ occurs) $$=$$ P(exactly one of the events $$B$$ or $$C $$ occurs) $$=$$ P(exactly one of the events $$C$$ or $$A$$ occurs) $$=$$ $$p$$ and P(all the three events occur simultaneously) $$=p^2$$, where $$0 < p < 1/2$$. Then the probability of at least one of the three events $$A, B$$ and $$C$$ occurring is

A bag contains $$a $$ white and $$b$$ black balls. Two players, $$A$$ and $$B$$ alternately draw a ball from the bag, replacing the ball each time after the draw till on of them draws a white ball and win the game. $$A$$ begins the game. If the probability of $$A$$ winning the game is three times that of $$B$$, the ratio $$a:b$$ is

For three events $$A, B$$ and $$C, P$$ (exactly one of the events $$A$$ occur) $$=$$ P (exactly one of the events B and C occur) $$=$$ P (exactly one of the events C or A occurs) $$=$$ p and P (all the three events occur simultaneously) $$=p^2$$, where $$0 < p < 1/2$$. If the probability of at least one of the three events $$A, B$$ and $$C$$ occurs is $$11/18$$, the value of $$p$$ is

If $$P(A)=0.7, P(B)=0.55, P(C)=0.5, P(A\cap B)=x, P(A\cap C)=0.45, P(B\cap C)=0.3$$ and $$P(A\cap B\cap C)=0.2$$, then

Only one subject

Three shots are fired at a target in succession. The probabilities of a hit in the first shot is $$\displaystyle \frac {1}{2}$$, in the second $$\displaystyle \frac {2}{3}$$ and in the third shot is $$\displaystyle \frac {3}{4}$$, In case of exactly one hit, the probability of destroying the target is $$\displaystyle \frac {1}{3}$$ and in the case of exactly two hits $$\displaystyle \frac {7}{11}$$ an in the case of three hits is $$1.0$$. Find the probability of destroying the target in three shots

A survey of people in a given region showed that $$20$$% were smokers. The probability of death due to lung cancer, given that a person smoked, was $$10$$ times the probability of death due to lung cancer, given that a person did not smoke. If the probability of death due to lung cancer in the region is $$0.006$$, what is the probability of death due to lung cancer given that a person is a smoker?

A pack contains 4 blue, 2 red and 3 black pens. If 2 pens are drawn at random from the pack, NOT replaced and then another pen is drawn. What is the probability of drawing 2 blue pens and 1 black pen?