A die is thrown, then find the probability of the following events:

A is an Event: getting an odd number on the top upper surface of the die.

B is an Event: getting a perfect square on the upper surface of the die.

Concept: Basic Ideas of Probability

There are three boys and two girls. A committee of two is to be formed. Find the probability of the following events:

Event A: The committee contains at least one girl

Event B: The committee contains one boy and one girl

Concept: Basic Ideas of Probability

In a certain race, there are three boys A, B, C. The winning probability of A is twice than B and the winning probability of B is twice than C. If P(A) + P(B) + P(C) = 1, then find the probability of win for each boy.

Concept: Basic Ideas of Probability

The divisor and quotient of the number 6123 are same and the remainder is half the divisor. Find the divisor.

Concept: Quadratic Equations Examples and Solutions

Find the class mark of the classes 20-30 and 30-40.

Concept: Basic Ideas of Probability

For a sequence if n `S_n=n/(n+1)` then find the value of S_{10}.

Concept: Introduction to Sequence

If two coins are tossed, then find the probability of the event that at least one head turns up.

Concept: Basic Ideas of Probability

Two digit numbers are formed using the digits 0, 1, 2, 3, 4, 5 where digits are not repeated.

P is the event that the number so formed is even.

Q is the event that the number so formed is greater than 50.

R is the event that the number so formed is divisible by 3.

Then write the sample space S and events P, Q, R using set notation.

Concept: Basic Ideas of Probability

The following data shows the number of students using different modes of transport:

Modes of Transport | Number of Students |

Bicycle | 140 |

Bus | 100 |

Walk | 70 |

Train | 40 |

Car | 10 |

From this table, find the central angle (θ) for the Mode of Transport ‘Bus’.

Concept: Tabulation of Data

Two coins are tossed simultaneously. Write the sample space ‘S’ and the number of sample points n(S). Write the following events using set notation and mention the number of elements in each of them:-

(a) A is the event of getting at least one head.

(b) B is the event of getting exactly one head

Concept: Basic Ideas of Probability

**There are three boys and two girls. A committee of two is to be formed. Find the probability of events that the committee contains :**

a) At least one girl.

b) One boy and one girl

c) Only boys

Concept: Basic Ideas of Probability

Find the class mark of the class 35 - 39.

Concept: Basic Ideas of Probability

Find the first two terms of the sequence for which S_{n} is given below: `S_n=n^2(n+1)`

Concept: Introduction to Sequence

Two coins are tossed simultaneously. Write the sample space (S), n(S), the following event A

using set notation and n(A), where ‘A is the event of getting at least one head.’

Concept: Basic Ideas of Probability

How many three digit natural numbers are divisible by 5?

Concept: Introduction to Sequence

Two dice are thrown. Find the probability of the event that the product of numbers on their upper faces is 12.

Concept: Basic Ideas of Probability

If one of the roots of the quadratic equation x^{2} - 11x + k = 0 is 9, then find the value of k

Concept: Quadratic Equations Examples and Solutions

Two dice are thrown. Find the probability of getting :

1) The sum of the numbers on their upper faces is at least 9.

2) The sum of the numbers on their upper faces is 15.

3) The number on the upper face of the second die is greater than the number on the upper face of the first die.

Concept: Basic Ideas of Probability

Write any two quadratic equations.

Concept: Quadratic Equations Examples and Solutions

**Decide whether the following equation is quadratic equation or not.**

x^{2} + 5x – 2 = 0

Concept: Quadratic Equations Examples and Solutions