Probability Tes...

One Indian and four American men and their wives are to be seated randomly around a circular table. Then, the conditional probability that the Indian man is seated adjacent to his wife given that each American man is seated adjacent to his wife is 

Each of the $$n$$ urns contains $$4$$ white and $$6$$ black balls. The $$(n+1)th$$ urn contains $$5$$ white and $$5$$ black balls. Out of the $$(n+1)$$ urns is chosen an urn at random and two balls are drawn from it without replacement. Both the balls turn out to be black. If the probability that the $$(n+1)th$$ urn was chosen to draw the ball is $$\displaystyle \frac { 1 }{ 6 } $$, then the value of $$n$$ is

A box contains  $$100$$  tickets numbered  $$1, 2, ....., 100$$. Two tickets are chosen at random. It is given that the minimum number on the two chosen tickets is not more than  $$10$$. The maximum number on them is  $$5$$  with probability.....

An unbiased coin is tossed. if the result is a head, a pair of unbiased dice is rolled & the number obtained by adding the numbers on the two faces is noted. If the result is a tail, a card from a well shuffled pack of eleven cards numbered  $$2, 3, 4,...., 12$$  is picked & the number on the card is noted. What is the probability that the noted number is either $$7$$  or $$8 $$?

A lot of contains $$20$$ articles. The probability that the lot contains exactly $$2$$ defective articles is $$0.4$$ and the probability that the lot contains exactly $$3$$ defective articles is $$0.6$$. Articles are drawn from the lot at random one by one without replacement and are tested till all defective articles are found. What is the probability that the testing procedure ends at the twelfth testing?

There are $$4$$ white and $$3$$ black balls in a box. In another box there are $$3$$ white and $$4$$ black balls. An unbiased dice is rolled. If it shows a number less than or equal to $$3$$, then a ball is drawn from the first box, but if it shows a number more than $$3$$, then a ball is drawn from the second box. If the ball drawn is black, then the probability that the ball was drawn from the first box is

Let $$\displaystyle H_{1},H_{2},H_{3},...,H_{n}$$ be mutually exclusive and exhaustive events with $$\displaystyle P\left ( H_{i} \right )> 0; i=1, 2, 3, ..., n.$$ Let E be any other event with $$\displaystyle 0 < P\left ( E \right )< 1.$$ 

For a biased die the probabilities for different faces to turn up are given below: The die is tossed and you are told that either face 1 or 2 has turned up. Then the probability that it is face 1 is .....

There are $$3$$ bags each containing $$5$$ white balls and $$2$$ black balls and $$2$$ bags each containing $$1$$ white balls and $$4$$ black balls, a black ball having been drawn, find the chance that it came from the first group.

There are two groups of subjects one of which consists of 5 science subjects and 3 engineering subjects and the other consists of 3 science and 5 engineering subjects. An unbaised die is cast. If number 3 or number 5 turns up, a subject is selected at random from the first group, other wise the subject is selected at random from the second group. Find the probability that an engineering subject is selected ultimately.