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Aptitude ➤ Probability ➤ Set 1
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.

Examples:
(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.

Details:
(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 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.

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

Examples:
(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}.

4. 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 ⊆ S.
∴ P(E) = n(E)n(s)

6. Results on Probability:
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 A denotes (not-A), then P(A) = 1 - P(A).
Question 11
Q11.  A box contains 5 green, 4 yellow, and 3 white marbles. Three marbles are drawn at random from the bag. What is the probability that they are not of the same colour.
Question 12
Q12.  A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is:
Question 13
Q13.  A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?
Question 14
Q14.  In a box, there are 7 red, 8 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?
Question 15
Q15.  A speaks truth in 75 % cases and B in 80 % of the cases. In What percentage of cases are they likely to contradict each other, narrating the same incident ?

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