Bag A contains 3 red and 4 black balls, and Bag B contains 5 red and 'n' black balls. One ball is drawn at random from one of the bags and it is found to be red. If the probability that it was from bag B is 35/68, then the value of 'n' is:

Let $F(z)$ be the cumulative density function of the standard normal variate $z$, then which of the following are correct?

(A) $F(z) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^z e^{-\frac{z^2}{2}} dz$, $-\infty < z < \infty$

(B) $F(-z) = 1 - F(z)$

(C) $F(0) = 0$

(D) $F(\infty) = 1$

Choose the correct answer from the options given below:

A can solve 90% problems and B can solve 70% problems of the book. A problem is selected at random from the book. The probability that the problem is solved, is equal to

Nitin has taken the subjects mathematics, physics and chemistry. The probability of him getting grade A in these subjects are respectively 0.2, 0.3 and 0.9. Getting grades in different subjects are regarded as independent events. The probability of getting A grade by him, either in mathematics or physics, is

Let A and B be two events. Then which of the following statements are TRUE?

(A) $P(B|A) = \frac{P(A \cap B)}{P(A)}$, provided $P(A) \neq 0$

(B) $P(B') = 1 + P(B)$

(C) $P(A \cup B) = P(A) + P(B) + P(A \cap B)$

(D) $P(A \cap B) = P(A).P(B)$ If A and B are independent events

Choose the correct answer from the options given below:

An insurance company insured 200 scooter drivers, 400 car drivers and 600 Truck drivers. The probability of an accident involving scooter driver, car driver and truck driver are 0.01, 0.03 and 0.15 respectively. One of the insured person meets an accident, then the probability that he is a truck driver is:-

If A and B are two events such that $P(A) \neq 0$, $P(B) \neq 1$ and $P(\bar{A}/\bar{B}) = \frac{1-k}{P(\bar{B})}$, then the value of $k$ is