## Probability Maths Notes

**Random Experiment**

An experiment in which all the possible results are known in advance, but none of them can be predicted with certainty, is called a random experiment.

The following are some examples of random experiment:

- Tossing a corn
- Throwing a die
- Drawing a card from a well-shuffled pack of 52 playing cards, etc.

**Outcome**

The result of a random experiment is called an outcome.

1. Tossing a corn, we have two possible outcomes. Head (H) or Tail (T).

2. Throwing a die, we have six possible outcomes. 1 or 2 or 3 or 4 or 5 or 6.

3. There are four suits in a pack of playing cards. Spades, hearts, diamonds and clubs. Each suit has 13 cards. Spade and Club are black cards. Heart and Diamond are red cards. King, Queen and Jack are called face cards. The card bearing number 1 is called Ace card. Ace card is not a face card. So we have fifty-two possible outcomes.

**Equally Likely Outcomes:**

A given number of outcomes are said to be equally likely, if none of them is expected to occur in preference to the others.

eg. when we toss a coin, the head or tail is the equally likely outcome.

**samp1e Space**

The set of all possible outcomes of a random experiment is called the sample space. A sample space is denoted by S or ‘Ω’ (omega). The number of elements in the set S (i.e. number of sample points) is denoted by n(S). The sample space is called a finite sample space, if n (S) is finite.

**Let’s Remember:**

- The sample space for a corn tossed twice is the same as that of two coins tossed simultaneously. The same is true for three coins.
- The sample space for a die rolled twice is the same as two dice are rolled simultaneously.

**Event**

The outcomes satisfying particular condition are called favourable outcomes.

A set of favourable outcomes, of a given sample space is an event.

Event is a subset of the sample space.

Events are generally denoted by capital letters A,B,C,D, etc. For example, if two coins are tossed and A is the event of getting at least one tail, then the favourable outcomes are as follows A = {TT, TH, HT}

The number of elements in the event A is denoted by n(A). Here n(A) = 3.

**For more information:**

Types of events:

- Certain event! Sure event
- Impossible event
- Simple! Elementary event
- Complement of an event
- Mutually exclusive events
- Exhaustive event

**Probability of an Event:**

The probability of an event A in a finite sample space S, is written as P(A) and is defined as

= \(\frac{n(A)}{n(S)}\)

**Let’s remember:**

- The probability is expressed as a fraction or a percentage.
- The probability of any event is from 0 to 1 or 0% to 100%.

If E is any event,

e.g. probability \(\frac{1}{4}\) is written as 25%.