Plus Two Maths Notes Chapter 13 Probability is part of Plus Two Maths Notes. Here we have given Plus Two Maths Notes Chapter 13 Probability.

Board | SCERT, Kerala |

Text Book | NCERT Based |

Class | Plus Two |

Subject | Maths Notes |

Chapter | Chapter 13 |

Chapter Name | Probability |

Category | Plus Two Kerala |

## Kerala Plus Two Maths Notes Chapter 13 Probability

**Conditional Probability**

- Probability of happening of an event A, given that B has already happened = P(A/B) Probability of happening of an event B, given that A has already happened = P(B/A)

provided P(A) ≠ 0)

**Properties**

. Let E and F be event of a sample spaces P(S|F) P (F|F) = l

. IfA and B are any two event of a sample space Sand F is an event of S (P (F) ≠ O),

then

. If A and B are disjoint event, then

. P(E|F) = l – P(E|F)

. Two events A & B are said to be independent if the occurrence of one does not affect the probability of occurrence or non-occurrence of the other.

**Multiplication rule of probably**

. From (1) and (2), we have

P (A∩B) = P (A|B) P (B) = P (B|A) P (A) ……………………(3)

Provided P (E) ≠ O and P (F) ≠ O.

. If events A and B are independent.

P(A|B) = P(A) and P(B|A) = P(B)

∴ In such a case,

P(A∩B) = P(A) × P(B) ………………..(4)

(3) & (4) are called the multiplication rule of probability.

. Multiplication rule for more than two events

P(F ∩ F ∩ G) = P(E) P(F|E) P(G|(E ∩ F))

= P (E) P (F|E) P (G|EF)

**Bayes’ Theorem**

. Theorem of total probability: Let {E_{1}, E_{2}, …, E_{n}} be a partition of the sample space

S. Let A be any event associated with S,

• Bayes’ theorem: If E_{1}, E_{2}, …, E_{n} are n non-empty events which constitute a partition of sample space S and A is any event of

non-zero probability, then

**Random Variable and Probability Destributlon**

. A discrete random variable is a variable which takes integral values depending upon the outcomes of the experiment. If x_{1}, x_{2}, x_{3} ……… x_{n} are the possible real number values associated to different exhaustive events of an experiment and p_{1}, p_{2}, p_{3}………. p_{n} are their respective probabilities, then distribution is represented as

(i) Mean

(ii) Variance

(iii) Standard Deviation

. Bernoulli trials: 1f the outcome of any trial is independent of the outcome of the other, then the probability of success or failure remains constant. The trial of such random experiment known as Bernoulli trials.

. Binomial Distribution, denoted by B(n, p) is given (q + p)^{n} where p represents prob ability of success, q represents probabil ity of non success and ‘n’ is the number of trials.

. Probability of r success, P(r) = ^{n}C_{n} q^{n-r} p^{r}, where n, p are parameters of the binomial distribution. P (r) is the probability function of the binomial distribution and

(q = I-p)

(i) Mean = np

(ii) Variance npq

(iii) Standard deviation

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