In the family mother, father and son stand up at random for a family picture. Define following two events :

$E$ = [Son stands at one of the two ends in the picture]

$F$ = [Father stands in the middle of the picture]

The value of $P(F/E)$ is :

A shopkeeper sells three types of flower seeds $A_1, A_2, A_3$. They are sold as a mixture where the proportions are 4 : 4 : 2 respectively. The germination rates of the three types of seeds are 45%, 60% and 35% respectively. Calculate the probability in the following cases.

The probability of a randomly chosen seed to germinate is :

Five dice are thrown simultaneously. If the occurrence of an even number in a single dice is considered a success, then the probability of at most 3 successes is

The curve $y = f(x)$ is normal probability curve, then which of the following statements are correct?

(A) mean, median and mode of the distribution coincide.

(B) the area bounded by the curve $y = f(x)$ and $x$-axis is one unit.

(C) The curve is symmetrical about the line $x = \mu$, where $\mu$ is the mean.

(D) $y$-axis is an asymptote to the curve.

Choose the correct answer from the options given below:

There are two bags. Bag-1 contains $4$ white and $6$ black balls and Bag-2 contains $5$ white and $5$ black balls. A die is rolled, if it shows a number divisible by 3, a ball is drawn from Bag-1, else a ball is drawn from Bag-2. If the ball drawn is not black in colour, the probability that it was not drawn from Bag-2 is :

If A and B are independent events, then which of the following statements are TRUE?

(A) $P(A \cap B) = P(A).P(B)$

(B) $P(A \cap B) = P(A) - P(B)$

(C) $P(A \cup B) = P(A) + P(B) - P(A).P(B)$

(D) $P(A \cap B) = P(A). P(B|A)$

Choose the correct answer from the options given below:

A bag contain 8 blue and 12 green balls. Two balls are drawn in succession without replacement. The probability that first is blue and second is green is