Probability

Question 1

Total number of outcomes when tossing ‘n’ coins

Answer 1

2ⁿ

Question 2

Total number of outcomes when throwing ‘n’ dices

Answer 2

6ⁿ

Question 3

Complementary events

Answer 3

Question 4

Impossible event

Answer 4

Event which is impossible and probability is zero

Question 5

Another name of sure event
also definition

Answer 5

Certain event
Event which is sure and probability is one

Question 6

Another name of certain event
also definition

Answer 6

Sure event
Event which is sure and probability is zero

Question 7

Total cards

Answer 7

52

Question 8

how many suit in deck of cards

Answer 8

4

Question 9

How many cards in each suit

Answer 9

13

Question 10

Explain all suits of deck

Answer 10

Question 11

Symbol and colour of club

Answer 11

♣ Black

Question 12

Symbol and colour of spade

Answer 12

♠ Black

Question 13

Symbol and colour of Diamond

Answer 13

♦Red

Question 14

Face Cards

Answer 14

Jack, Queen, King (4x3=12)

Question 15

Number Cards

Answer 15

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

Question 16

Honor Cards

Answer 16

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

Question 17

Equally Likely Events

Answer 17

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

Question 18

Mutually Exclusive Events

Answer 18

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

Question 19

Condition of mutually exclusive events

Answer 19

A∩B = ϕ
P(A∩B) = 0

Question 20

Exhaustive events

Answer 20

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.

Question 21

Sample space to tossing 4 coins simultaneously

Answer 21

Question 22

Odd against

Answer 22

Question 23

Odd in favour

Answer 23

Question 24

What to to do in Random Drawn (Two or more)

Answer 24

Use Combination

Question 25

Where to use combination in probability

Answer 25

Random Drawn (Two or more)

Question 26

In mutual exclusive P(A∩B∩C)

Answer 26

0

Question 27

In mutual exclusive P(AUBUC)

Answer 27

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

Question 28

Dead Heat

Answer 28

Draw

Question 29

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

Answer 29

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

Question 30

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

Answer 30

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.

Question 31

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

Answer 31

They are Mutually Exclusive and Exhaustive Events.

Question 32

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

Answer 32

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

Question 33

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

Answer 33

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

Question 34

Dead heat is impossible means

Answer 34

Events are mutually exclusive

Question 35

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

Answer 35

“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.

Question 36

at least one of the events must occur means

Answer 36

Events are exhaustive

Question 37

Conditional Probability

Answer 37

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

Question 38

P(A/B) = ? (Formula)

Answer 38

Question 39

P(B/A) = ? (Formula)

Answer 39

Question 40

read the answer

Answer 40

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