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Probability and Statistics > Probability > Flashcards

Probability Flashcards

1
Q

Total number of outcomes when tossing ‘n’ coins

A

2ⁿ

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2
Q

Total number of outcomes when throwing ‘n’ dices

A

6ⁿ

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3
Q

Complementary events

A
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4
Q

Impossible event

A

Event which is impossible and probability is zero

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5
Q

Another name of sure event
also definition

A

Certain event
Event which is sure and probability is one

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6
Q

Another name of certain event
also definition

A

Sure event
Event which is sure and probability is zero

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7
Q

Total cards

A

52

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8
Q

how many suit in deck of cards

A

4

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9
Q

How many cards in each suit

A

13

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10
Q

Explain all suits of deck

A
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11
Q

Symbol and colour of club

A

♣ Black

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12
Q

Symbol and colour of spade

A

♠ Black

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13
Q

Symbol and colour of Diamond

A

♦Red

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14
Q

Face Cards

A

Jack, Queen, King (4x3=12)

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15
Q

Number Cards

A

2, 3, 4, 5, 6, 7, 8, 9, 10 (except ace)
[4x9=36]

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16
Q

Honor Cards

A

Ace + Face cards = Honor Cards
Ace, Jack, Queen, King
[4x4=16]

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17
Q

Equally Likely Events

A

Two or more events are said equally likely if each one of them has an equal chance of occurrence

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18
Q

Mutually Exclusive Events

A

(Doesn’t happen simultaneously)
Two or more events are mutually exclusive if the occurrence of each event prevents the every other event

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19
Q

Condition of mutually exclusive events

A

A∩B = ϕ
P(A∩B) = 0

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20
Q

Exhaustive events

A

All the events are exhaustive events if their union is sample space
E₁U E₂U E₃ …. Eₙ = S
P(E₁U E₂U E₃ …. Eₙ) = 1
When events are exhaustive, it guarantees that at least one of the events must occur because they collectively cover all possible outcomes of the experiment.
* When a sample space is distributed down into some mutually exclusive events such that their union forms the sample space itself, then such events are called exhaustve events

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21
Q

Sample space to tossing 4 coins simultaneously

A
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22
Q

Odd against

A
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23
Q

Odd in favour

A
24
Q

What to to do in Random Drawn (Two or more)
Also random means

A

Use Combination
Not one by one (simultaneously)

25
Q

Where to use combination in probability

A

Random Drawn (Two or more)

26
Q

In mutual exclusive P(A∩B∩C)

A

0

27
Q

In mutual exclusive P(AUBUC)

A

P(A) + P(B) + P(C)

28
Q

Dead Heat

A

Draw

29
Q

If E₁, E₂, E₃,…….Eₙ are mutual exclusive events then
Probability that any one of them occurs = ?

A

P(one of them occur) = P(E₁) + P(E₂) + P(E₃) +…….+P(Eₙ)

30
Q

If E₁, E₂, E₃,…….Eₙ are the events and P(one of them occur) = P(E₁) + P(E₂) + P(E₃) +…….+P(Eₙ)
What it tells about events

A

1.)The events are mutually exclusive: The probability of their intersection is 0, so there’s no overlap to account for.
2.)The events are exhaustive: At least one of them must occur.

31
Q

What does it mean if events E₁, E₂, E₃,…….Eₙ
are such that one must happen and only one can happen at a time?

A

They are Mutually Exclusive and Exhaustive Events.

32
Q

If odd against ratio of A = m:n
Prob(A) = ?
(Derive it)

A

P(A) = n / (m+n)

33
Q

If odd in favour of A = m:n
Prob(A) = ?
(Derive it)

A

P(A) = m / (m+n)

34
Q

Dead heat is impossible means

A

Events are mutually exclusive

35
Q

“a dead heat is impossible” effectively enforces the ________________, but it’s not necessarily the same as being ___________________.

A

“a dead heat is impossible” effectively enforces the mutual exclusivity condition, but it’s not necessarily the same as being exhaustive unless all possible outcomes are explicitly listed.

36
Q

at least one of the events must occur means

A

Events are exhaustive

37
Q

Conditional Probability

A

Let A and B are two events with same random experiment. Then the probability of occurrence of event A when event B has already occurred is called the conditional probability.

P(A/B) = Probability of event A given that B has already occured
P(B/A) = Probability of event B given that A has already occurred

38
Q

P(A/B) = ? (Formula)

A
39
Q

P(B/A) = ? (Formula)

A
40
Q

read the answer

A

If there is a question of compound experiment, create sample space because the question of compound experiment solved by sample space

41
Q

Keywords for multiplication law of probability

A
  • successively
  • One by one without replacement
  • Dependent event
42
Q

Multiplication law of probability

A

If A and B are two events associated with same random experiment. The probability of simultaneously occurrence of two events A and B is equal to the probability of one of the two events multiplied by the conditional probability of other.
P(A∩B) = P(AB) = P(A) P(B/A) or P(B) (A/B)

43
Q

without replacement and combination point

A

Use combination in without replacement (no need to make cases)
in without replacement there is no difference between one by one and simultaneously

44
Q

Where can’t we use combination

A

in replacement

45
Q

Range of P(AUB)

A

max(P(A),P(B))≤P(A∪B)≤P(A)+P(B)

46
Q

Maximum value of P(AUB) and why?

A

Maximum of P(AUB) = max(P(A), P(B))
Reason:
If A and B are mutually exclusive i.e. P(A∩B) =0
then P(A∪B)=P(A)+P(B).

47
Q

Minimum value of P(AUB) and why?

A

Minimum of P(AUB) =max(P(A),P(B))
Reason:
If A s subset of B (or vice versa), meaning P(A∩B) = P(A) (or P(B)).
In this case, the union is essentially the larger event because one set is contained within the other.

48
Q

If P(A) = 1, regardless of P(B)
What is P(AUB)

A

A is a certain event, so P(AUB) = 1 regardless of P(B)

49
Q

How does the probability of A∩B compare to P(A)?

A

P(A∩B)≤P(A)
By definition,A∩B is a subset of A, so the probability of A∩B cannot exceed the probability of A.
This principle is part of the monotonicity of probability, which states that the probability of a subset is always less than or equal to the probability of the entire set.

50
Q

Keyword for independent events

A

with replacement

51
Q

Independent events

A

Two events are associated with a random experiment are said to be independent if the occurrence of one event does not effect the probability of occurrence of other.
P(A∩B) = P(A).P(B)

52
Q

If A and B are independent events, then P(A/B) and P(B/A) = ?
and why?

A

If A and B are independent events,
then P(A/B) = P(A) [B se koi affect nahi padh rha A ko]
and P(B/A) = P(B)

53
Q

Note for independent events

A
54
Q

What is the formula for
P(onlyApasses) if A and B are independent?

A

P(onlyApasses)=P(A)⋅(1−P(B)).

55
Q

What is the formula for
P(onlyApasses) if A and B are dependent?

A

P(onlyApasses)=P(A)⋅P(B’∣A),
where
P(B′∣A)=1−P(B∣A).

56
Q

What is
P(onlyApasses) if A and B are mutually exclusive?

A

P(onlyApasses)=P(A),
because P(A∩B)=0 (A and B cannot occur together).

Probability and Statistics (5 decks)

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