Lecture-5 Probability and Chi – square

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OUTLINE NOTES
प्रायिकता व काई – वर्ग (Probability and Chi – square):-
प्रायिकता (Probability):- किसी विशेष घटना के घटित होने की संभावना को उस घटना की प्रायिकता कहते हैं।
(The possibility of an event to occur is called the probability of that event.)
1. घटनाओं के प्रकार (Types of Events):- 2 प्रकार हैं –
(2 types -)
i. स्वतंत्र घटनाएँ (Independent Events):- ऐसी घटनाएँ जिनके घटित होने पर दूसरी घटनाओं के घटने पर कोई प्रभाव नहीं पड़ता है, तो ये स्वतंत्र घटनाएँ कहलाती हैं।
(Events whose occurrence has no effect on the occurrence of other events are called independent events.)
ii. संबन्धित घटनाएँ (Dependent Events):- ऐसी घटनाएँ जिनके घटित होने पर दूसरी घटनाओं के घटने पर प्रभाव पड़ता है, तो ये संबन्धित घटनाएँ कहलाती हैं।
(Events whose occurrence has an effect on the occurrence of other events are called dependent events.)
2. नियम (Rules):-
i. Rule of Addition:- यदि किसी एक घटना के 2 या अधिक भिन्न तरीकों से होने की संभावना निकालनी हो तो प्रायिकतायों को जोड़ दिया जाता है। पहचान = ‘या’
(If the probability of an event occurring in 2 or more different ways is to be determined, then the probabilities are added. Identification = 'or')
उदाहरण:- एकल संकर संकरण में F2 पीढ़ी में सभी लम्बे पौधे आने की प्रायिकता
(Example:- Probability of getting all tall plants in F2 generation in a monohybrid cross)
ii. Rule of Multiplication:- यदि दो या अधिक स्वतंत्र घटनाओं के साथ – साथ होने की प्रायिकता निकालनी हो तो गुना करते हैं। पहचान = ‘और’
(If we want to find the probability that two or more independent events occur together, then probabilities are multiplied. Identification = 'and')
उदाहरण:- द्वि संकर संकरण में F2 पीढ़ी में TtRr जीन प्रारूप आने की प्रायिकता
(Example:- Probability of getting TtRr genotype in F2 generation in a dihybrid cross)

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