Aptitude ➤ Probability

An operation which can produce some well-defined outcomes is called an experiment.

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

(a) Rolling an unbiased dice.

(b) Tossing a fair coin.

(c) Drawing a card from a pack of well-shuffled cards.

(d) Picking up a ball of certain colour from a bag containing balls of different colours.

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

(b) 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.

(c) A pack of cards has 52 cards.

It has 13 cards of each suit, name

Cards of spades and clubs are

Cards of hearts and diamonds are

There are 4 honours of each unit.

There are

When we perform an experiment, then the set S of all possible outcomes is called the

(a) In tossing a coin, S = {H, T}

(b) If two coins are tossed, the S = {HH, HT, TH, TT}.

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

Any subset of a sample space is called an event.

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

Then, E ⊆ S.

∴ P(E) =

P(S) = 1

0 ≤ P (E) ≤ 1

P(ϕ) = 0

For any events A and B we have : P(A ⋃ B) = P(A) + P(B) - P(A ⋂ B)

If

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