An urn contains $7$ red, $5$ white and $3$ black balls. Three balls are drawn randomly one after the other without replacement. If it is known that the first ball drawn is red and the second ball drawn is white, then the probability that the third ball drawn is not red is

One card is missing in a pack of $52$ playing cards. If two cards are drawn randomly from the remaining cards at a time and are found to be spades,then the probability that the missing card is not a spade is

In four schools $B_1, B_2, B_3, B_4$,the percentage of girl students is $12, 20, 13, 17$ respectively. From a school selected at random,one student is picked up at random and it is found that the student is a girl. The probability that the school selected is $B_2$ is:

Two coins are available, one fair and the other two-headed. Choose a coin and toss it once; assume that the unbiased coin is chosen with probability $\frac{3}{4}$. Given that the outcome is head, the probability that the two-headed coin was chosen, is

The probability of men getting a certain disease is $\frac{1}{2}$ and that of women getting the same disease is $\frac{1}{5}$. The blood test that identifies the disease gives the correct result with probability $\frac{4}{5}$. Suppose a person is chosen at random from a group of $30$ males and $20$ females,and the blood test of that person is found to be positive. What is the probability that the chosen person is a man?

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