Probability Tes...

If two events $$A$$ and $$B$$ are such that $$P\left( \overline { A }  \right) =0.3,P\left( B \right) =0.5$$ and $$P\left( A\cap B \right) =0.3$$, then $$\displaystyle P\left( \frac { B }{ A\cup \overline { B }  }  \right) $$ is equal to

The chances of defective screws in three boxes $$A,B,C$$ are $$\displaystyle \frac { 1 }{ 5 } ,\frac { 1 }{ 6 } ,\frac { 1 }{ 7 } $$ respectively. A box is selected at random and a screw drawn from it at random from it is found defective. The probability that it came from the box $$A$$ is

There are two bags, one of which contains three black and four white balls while the other contains four black and three white balls. A die is cast: if the face 1 or 3 turns up, a ball is taken from the first bag; and if any other face turns up, a ball is chosen from the second bag. Find the probability of choosing a black ball.

Two coins are tossed. What is the conditional probability that two heads result, given that there is at least one head ?

Consider a family with two children. Assume that each child is as likely to be a boy as it is to be a girl. Find the conditional probability that both children are boys, given that one child is a boy

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.

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 two events A and B such that $$P(A')=0.3, P(B)=0.5$$ and $$P(A\cap B)=0.3$$, then $$P(B|A \cup B')$$ is

If $$A$$ and $$B$$ are mutually exclusive events, then $$\displaystyle P\left ( A \right )> 0$$ and $$\displaystyle P\left ( B \right )\neq 1,$$ $$\displaystyle P\left ( \overline{A/B} \right )$$ is equal to