Probability is defined as feasibility of happening an event. In other way also we can defined as below.

The possibility of happening or not happening of an event is known as probability.

**Possibility of happening of an event** = **${\text"Number of favourable outcomes"} / {\text"Total number of outcomes"}$**

**Experiment:** It is an action where result is uncertain

**Sample space:** It is set of all the possible outcomes of that experiment. Denoted by ‘S’

**Example**: If we toss a coin, sample space = {Head, Tail}

**Event**: Event is the result of an experiment

**Mutually Exclusive Events:** Two events are called mutually exclusive events when they cannot occur at the same time.

**Dependent Events**: Two events are called Dependent events when the outcome of the first event should affect the outcome of second event.

**Independent Events**: Two events are called Independent events when the outcome of the first event should not affect the outcome of second event.

**Elementary event**: An event having only one outcome of the experiment is called an elementary event.

1. Probabilities are expressed as **fractions, decimal fractions or percentages .**

2. An** outcome** is the result of an action such as throwing a die or picking a card from a pack.

3. For equally likely outcomes, the probability of the event E occurring is given by Probability of event E happening =${\text"Numer of ways that event occurs"}/{\text"Total number of possible outcomes"}$

**4. The sum of the probabilities of all the elementary events of an experiment is 1.**

**i.e. If we three elementary event A,B,C in the experiment ,then**

**$P(A)+P(B)+P(C)=1$**

**5. The event $\ov{A}$ representing ‘not A’, is called the complement of the event A. We also say that A and $\ov{A}$ are complementary events. Also P(A)+P($\ov{A}$)=1**

6. The probability of an event (U) which is impossible to occur is 0. Such an event is called an impossible event

**$P(U)=0$**

**7. The probability of an event ( X) which is sure (or certain) to occur is 1. Such an event is called a sure event or a certain event**

**$P(X)=1$**

**8. Probability of any event can be as $0≤P≤1$**

Probability Online Practice test

Example 1 |
Answer |

When a die is tossed, what is the probability that a 5 or a 6 will face up? |
Total six possible outcomes = {1, 2, 3, 4, 5, 6} Required two outcomes= {5, 6} P(E) = $2/6$ =$1/3$ |

Example 2 |
Answer |

A card is picked from a normal pack of 52. What is the probability the card will be a heart? |
There are 52 cards in a pack. There are 13 hearts. P(Heart) = $13/52$ = |

Online Test - 1 (Probability) TAKE TEST
Number of questions : 20 | Time : 30 minutes |

Online Test - 2 (Probability) TAKE TEST
Number of questions : 20 | Time : 30 minutes |

Online Test - 3 (Probability) TAKE TEST
Number of questions : 20 | Time : 30 minutes |

Online Test - 4 (Probability) TAKE TEST
Number of questions : 20 | Time : 30 minutes |

Online Test - 5 (Probability) TAKE TEST
Number of questions : 20 | Time : 30 minutes |

**Direction:**

A basket contains 4 red, 5 blue and 3 green marbles.

**Question-1)****If two marbles are drawn at random, what is the probability that both are red?**

A) $3 / 7 $

B) $1 / 2 $

C) $2 / 11 $

D) $1 / 6 $

E) None of these

Ans: E

Solution:

According to the formulae,

Possibility of happening of an event = ${\text"Number of favourable outcomes"} / {\text"Total number of outcomes"}$

$({^4c_2} / {^12c_2}) = 6/66 = 1 / 11$

**Question-2)**

**If three marbles are picked at random, what is the probability that at least one is blue?**

A) $7 / 12$

B) $37 / 44$

C) $5 / 12$

D) $7 / 44$

E) None of these

Ans: B

Solution:

As per given data, total number of possible outcomes = ${^{12}c_3}$ = 220

Number of events that do not contain blue marbles = ${^7c_3}$ = 35

Probability = $[1 – (35/220)]$ = $37/44$