For the following questions answer them individually
If the mean and mode of a data are 45 and 51 respectively then the median of the data is
If $$\sigma$$ is the standard deviation of the observations $$x_1, x_2, ........., x_n$$ then the standard deviation of $$5x_1 + 7, 5x_2 + 7, ......, 5x_n + 7$$ is
If two unbiased six-faced dice are thrown simultaneously then the probability that the sum is 8 with at least one die showing a prime number is
If A and B are events of a random experiment with $$P(A) = \frac{3}{8}, P(B) = \frac{1}{3}$$ and $$P(A \cap B) = \frac{1}{4}$$ then $$P(\overline{A} \cap \overline{B}) =$$
A group has 12 men and 4 women. If three were selected at random from the group then the probability that they are all men is