$A$ card from a pack of $52$ cards is lost. From the remaining $51$ cards,$n$ cards are drawn and are found to be spades. If the probability of the lost card being a spade is $\frac{11}{50}$,then $n$ is equal to

$A$ student has to write the words $ABILITY$, $PROBABILITY$, $FACILITY$, $MOBILITY$. He wrote one word and erased all the letters in it except two consecutive letters. If '$LI$' is left after erasing, then the probability that the boy wrote the word $PROBABILITY$ is

There are three bags $X$,$Y$,and $Z$. Bag $X$ contains $5$ one-rupee coins and $4$ five-rupee coins; Bag $Y$ contains $4$ one-rupee coins and $5$ five-rupee coins; and Bag $Z$ contains $3$ one-rupee coins and $6$ five-rupee coins. $A$ bag is selected at random and a coin drawn from it at random is found to be a one-rupee coin. Then the probability that it came from bag $Y$ is:

$A$ manufacturing company of bulbs has $3$ units $A, B$ and $C$ which produce $25 \%$,$35 \%$ and $40 \%$ of the bulbs respectively. Out of the bulbs produced by $A, B, C$ units,$5 \%, 4 \%$ and $2 \%$ are defective respectively. If a bulb is chosen at random and found to be defective,then the probability that it is produced by unit $B$ is

In a manufacturing company,three machines $A$,$B$ and $C$ respectively produce $20 \%$,$30 \%$ and $50 \%$ of the total product. The defective products from $A$,$B$ and $C$ are respectively $5 \%$,$3 \%$ and $2 \%$. If an article produced by the company is selected at random and is found to be defective,then the probability that it is produced by machine $B$ is

In answering a question on a multiple choice test,a student either knows the answer or guesses. Let $\frac{3}{4}$ be the probability that he knows the answer and $\frac{1}{4}$ be the probability that he guesses. Assuming that a student who guesses at the answer will be correct with probability $\frac{1}{4}$. What is the probability that the student knows the answer given that he answered it correctly?