2. Probability
How likely something is to happen.
All probabilities are between 0 and 1.
Event
Simple Event
Sample Space
Formula =
P(A) = n(A)/n(S)
4. Conditional Probability
If A and B are two events associated with the same sample space of
a random experiment, the conditional probability of event A given
that B has occurred is given by p(A/B)=P( A ∩ B ) / P( B ), provided
P( B ) ≠ 0.
Formula =
P(A | B) = P(A ∩ B) / P(B) ( P(B) ≠ 0 )
P(B | A) = P(A ∩ B) / P(A) ( P(A) ≠ 0 )
5. Independent Events and Dependent Events
Independent Event
- The outcome of one event does
not affect the outcome of the
other event.
- Formula =
- P( A ∩ B ) = P( A ) * P( B )
Dependent Event
- The outcome of one event does
influence the outcome of the other
event.
- Formula =
- P( A ∩ B ) = P( A ) * P( B after A )
6. Mutually exclusive events
The events are mutually exclusive if they don’t occur same time or
simultaneously.
Formula =
P (A ∪ B) = P(A) + P(B)
7. Probability Distribution
Random Variable = X
- A type of variable in statistics whose possible values depend on the
outcomes of a certain random phenomenon.
• Probability Distribution = P(X)
- If a random variable x takes values x1, x2, …., xn with respective
probability p1, p2, …., pn, then is known as the probability distribution of
X.
Formula =
𝑖=1
𝑛
𝑝𝑖 = 1
X X1 X2 …….. Xn
P(X) P1 P2 …….. Pn
18. Application of probability
Flipping a coin
Choosing a card from the deck
Throwing a dice
Pulling a green candy from a bag of red candies
Winning a lottery 1 in many millions
Weather forecasting
Calculation of batting average in cricket