Probability Tes...

In a bolt factory, machines A, B and C manufacture 25%, 35%, 40% respectively. Of the total of their output 5, 4 and 2% are defective. A bolt is drawn and is found to be defective. What are the probabilities that it was manufactured by the machines A, B and C?

If in Q. 104, we are told that a white ball has been drawn, find the probability that it was drawn from the first urn.

If $$A$$ and $$B$$ are mutually exclusive events, then $$\displaystyle P\left ( A\cap B \right )$$ equals

Two coins are tossed, $$A$$ is the event of getting at most one head, $$B$$ is the event getting both heads, $$C$$ is the event of getting same face on both the coins. The events $$A$$ and $$B$$ are:

A is known to tell the truth in $$5$$ cases out of $$6$$ and he states that a white ball was drawn from a bag containing $$8$$ black and $$1$$ white ball. The probability that the white ball was drawn, is

If $$P(E_k)=C$$ for $$0\leq k\leq n$$, then the probability that $$X$$ is the only student to pass the examination is

A certain player, say $$X$$, known to win with probability $$0.3$$ if the track is fast and $$0.4$$ if the track is slow. For Monday, there is a $$0.7$$ probability of a fast track and $$0.3$$ probability of a slow track. The probability that player $$X$$ will win a Monday, is

At the college entrance examination each candidate is admitted or rejected according to whether he has passed or failed the tests. Of the candidate who are really capable, $$80$$% pass the test and of the incapable, $$25$$% pass the test. Given that $$40$$% of the candidates are really capable, then the proportion of capable college students is about 

A die is thrown. $$A$$ is the event that prime number comes up, $$B$$ is the event that the number divisible by three comes up, $$C$$ is the event that the perfect square number comes up. Then, $$A, B$$ and $$C$$ are :

A person is know to speak the truth 4 times out of 5. He throws a die and reports that it is a ace. The probability that it is actually a ace is