Probability

The examples of the probability include - flipping a coin, rolling a die, drawing a card from a deck, and picking a ball from a bag.

There are various applications of the probability in the real life. It is used to take informed decisions and risks in the following areas - insurance, weather forecasting, finance, business, sports, computer Science and gaming.

There are two basic rules for finding the Probability of two events A and B - Multiplication Rule and Addition Rule. 

There are four types of probability - Classical, Empirical, Subjective, and Axiomatic Probability. The classical probability is based on the logical and known outcomes, Empirical are based on data from actual experiments, and subjective is based on intuition, personal opinion, or experience.

Probability in Maths is used to calculate how an event is likely to occur. It is measured by dividing the favorable outcomes number by the number of possible outcomes. It is expressed from 0% to 100% or by either 0 (impossible) or 1 (certain).

A: 3 numbers are in A.P.
B: 3 numbers are even
P (B/A) = n (A ∩ B) / n (A) = (²? C? + ²? C? ) / (? C? +? C? ) = (25 × 24) / (50 × 49) = 12/49

5 red, 3 yellow
There are 3 points in sample space either both are red or both are yellow or one is red other is yellow.
⇒ P (E) = (3.5+5.3) / (3.5+5.3+5.4+3.2) = 15/28

Initial mean of 25 observations is 40.
X? = (Σx? )/25 = 40 => Σx? = 25 * 40 = 1000.

A teacher of age 60 retires.
The new sum of ages for the remaining 24 people is 1000 - 60 = 940.

A new teacher of age x joins.
The new sum for 25 people is 940 + x.
The new mean is 39.
(940 + x) / 25 = 39
940 + x = 39 * 25

n (s) = 6² = 36
E = { (1, 1), (1, 2), (1, 3), (1, 5), (1, 7), (2, 1), (2, 2), (2, 3), (2, 5), (3, 1), (3, 2), (3, 3), (3, 5), (5, 1), (5, 2), (5, 3), (7, 1)}
∴ n (E) = 17
Required prob. = n (E) / n (S) = 17 / 36