Consider an experiment of tossing 3 coins simultaneously. Define the following events:

$E$ = [Three heads or three tails appear]

$F$ = [At least two heads appear] and

$G$ = [At most two heads appear]

Choose the correct option:

4 cards are drawn from a standard deck of 52 cards. The probability of drawing exactly 2 cards of the same suit is:

If $y$ is normal distribution random variable with mean $\mu = 10$ and standard deviation $\sigma = 2$. $z$ is standard normal variable and $F(Z)$ is cumulative distribution function, then which of the following are true?

[Given that $F(1.5) = 0.9332$, $F(3) = 0.9986$, $F(2.25) = 0.9878$ and $F(1) = 0.8413$]

(A) $P(X < 13) = 0.9332$

(B) $P(X > 16) = 0.9986$

(C) $P(12 < X < 14.5) = 0.1465$

(D) $P(X > 8) = 0.8413$

Choose the correct answer from the options given below:

If A and B are two events such that $P(A) = \frac{1}{2}$, $P(B) = \frac{1}{3}$ and $P(A \cap B) = \frac{1}{4}$, then which of the following statements are true?

(A) A and B are independent events

(B) $P(A | B) = \frac{3}{4}$

(C) $P(A' | B') = \frac{5}{8}$

(D) $P(A' | B) = \frac{1}{4}$

Choose the correct answer from the options given below:

A green and a yellow dice are rolled in order, then the probability that a sum greater than 9 is

The binomial distribution for which the mean is 5 and variance 4, is

If A and B are two independent events such that P(A) = 1/3, $P(A\cup B) = 3/5$ and P(B) = p, then which of the following are true?

(A) The value of p is $\frac{2}{5}$

(B) $P(A\cap B) = \frac{2}{15}$

(C) $P(B/A) = \frac{1}{3}$

(D) $P(A/B) = \frac{3}{5}$

Choose the correct answer from the options given below: