# Probability Questions

**FACTS AND FORMULAE FOR PROBABILITY QUESTIONS**

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**1. Experiment : **An operation which can produce some well-defined outcomes is called an experiment.

**2. Random Experiment :**An experiment in which all possible outcomes are know and the exact output cannot be predicted in advance, is called a random experiment.

**Ex :**

**i. **Tossing a fair coin.

**ii.** Rolling an unbiased dice.

**iii. **Drawing a card from a pack of well-shuffled cards.

**3. Details of above experiments:**

**i.** When we throw a coin, then either a Head (H) or a Tail (T) appears.

**ii.** A dice is a solid cube, having 6 faces, marked 1, 2, 3, 4, 5, 6 respectively. When we throw a die, the outcome is the number that appears on its upper face.

**iii.** A pack of cards has 52 cards.

- It has 13 cards of each suit, name Spades, Clubs, Hearts and Diamonds.
- Cards of spades and clubs are black cards.
- Cards of hearts and diamonds are red cards.

There are 4 honours of each unit. There are Kings, Queens and Jacks. These are all called face cards.

**4. Sample Space: **When we perform an experiment, then the set S of all possible outcomes is called the sample space.

**Ex :**

**1.** In tossing a coin, S = {H, T}

**2.** If two coins are tossed, the S = {HH, HT, TH, TT}.

**3.** In rolling a dice, we have, S = {1, 2, 3, 4, 5, 6}.

**Event : **Any subset of a sample space is called an event.

**5. Probability of Occurrence of an Event : **

Let S be the sample and let E be an event.

Then, $E\subseteq S$

$\therefore P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}$

**6. Results on Probability :**

**i.** P(S) = 1 **ii.** $0\le P\left(E\right)\le 1$ **iii.** $P(\varnothing )=0$

**iv.** For any events A and B we have :

$P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$

**v.** If $\overline{)A}$ denotes (not-A), then $P\left(\overline{)A}\right)=1-P\left(A\right)$