From a group of 2 boys and 3 girls, two children are selected at random. Describe the following events associated with the above experiment. `E_4` both the selected children are girls.

From a group of 2 boys and 3 girls, two children are selected at random. Describe the event : A: both selected children are girls

From a group of 2 boys and 3 girls, two children are selected at random. Describe the event : C: at least one boy is selected.

From a group of 2 boys and 3 girls, two children are selected at random. Describe the event : B: the selected group consists of one boy and one girl.

From a group of 2 men and 3 women, two persons are selected. Describe the sample space of the experiment. If E is the event in which one man and one woman are selected, then which are the cases favourable to E ?

Two dice are thrown and the sum of the numbers which come up on the dice is noted. Let us consider the following events associated with this experiment : A : the sum is even B : the sum is a multiple of 3 C : the sum is less than 4 D : the sum is greater than 11. Which of these events are mutually exclusive ?

A class consists of 10 boys and 8 girls. Three students are selected at random. Find the probability that the selected group has : all girls.

A class consists of 10 boys and 8 girls. Three students are selected at random. Find the probability that the selected group has : all Boys.

In a family, with two children, the probability of both children are girls is:

If E_1 and E_2 are two independent events associated with an experiment, then show that E_1^c and E_2^c are alos independent.

A class consists of 10 boys and 8 girls. Three students are selected at random. Find the probability that the selected group has : 2 boys and 1 girl.