Probability Tes...

In a box containing $$100$$ are defective. The probability that out of a sample of $$5$$ bulbs, none is defective is:

One ticket is selected randomly from the set of $$100$$ tickets numbered as $$\left\{00, 01, 02, 03,04,05,...,98, 99\right\}$$. $$E_1$$ and $$E_2$$ denote the sum and product of the digits of the number of the selected ticket. The value of $$P \left(\displaystyle \frac{E_{1}=9}{E_{2}=0} \right)$$ is

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

lt is given that the events $$\mathrm{A}$$ and $$\mathrm{B}$$ are such that $$P(A)=\displaystyle \frac{1}{4}, P(\displaystyle \frac{A}{B})=\frac{1}{2}$$ and $$P(\displaystyle \frac{B}{A})=\frac{2}{3}$$ then $$\mathrm{P}(\mathrm{B})=$$

A lot contains 20 articles. The probability that the lot contains exactly 2 defective articles is 0.4 and the probability that it contains exactly 3 defective articles is 0.6. Articles are drawn from the lot at random one by one, without replacement and tested till all defective articles are found. The probability that the testing procedure ends at the 12th testing is

A letter is known to have come form TATANAGAR or CALCUTTA. On the envelope just two consecutive letters TA are visible. The probability that the letter has come from CALCUTTA is

A bag contains some white and some black balls, all of which are distinguishable from each other, all combinations of balls being equally likely. The total number of balls in the bag is $$10$$. If three balls are drawn at random and all of them are found to be black, the probability that the bag contains $$1$$ white and $$9$$ black balls is :

A man is known to speak the truth $$3$$ out of $$4$$ times. He throws a die and reports that it is a six. The probability that it is actually a six is

5 cards are drawn at random from a well shuffled pack of 52 playing cards. If it is known that there will be at least 3 hearts, the probability that there are 4 hearts is

5 cards are drawn at random from a well shuffled pack of 52 playing cards. If it is known that there will be at least 3 hearts, the probability that there are exactly 3 hearts is