Kerala Board Solutions for Chapter: Mathematics of Chance, Exercise 4: Exercise 4

In class $10 \mathrm{A}$, there are $30$ boys and $20$ girls. In class $10 \mathrm{B}$, there are $15$ boys and $25$ girls. One student is to be selected from each class.
What is the probability of both being girls?

In class $10 \mathrm{A}$, there are $30$ boys and $20$ girls. In class $10 \mathrm{B}$, there are $15$ boys and $25$ girls. One student is to be selected from each class.
What is the probability of both being boys?

In class $10 \mathrm{A}$, there are $30$ boys and $20$ girls. In class $10 \mathrm{B}$, there are $15$ boys and $25$ girls. One student is to be selected from each class.
What is the probability of at least one boy?

One is asked to say a two-digit number. What is the probability of both digits being the same?

One is asked to say a two-digit number. What is the probability of the first digit being larger? 

One is asked to say a two-digit number. What is the probability of the first digit being smaller? 

Each two-digit number is written on a paper slip and these are all put in a box. What is the probability that the product of the digits of a number drawn is a prime number? What if three-digit numbers are used instead?

Two dice with faces numbered from $1$ to $6$ are rolled together. What are the possible sums? Which of these sums has the maximum probability?