Prayikta Class 10 Notes — Chapter Ka Quick Overview
Agar aap prayikta class 10 notes dhoondh rahe hain, to yeh article aapke liye hi hai. Class 10 Maths ka Chapter 13 (Probability / Prayikta) NCERT rationalized syllabus ka ek scoring chapter hai — ismein koi lamba proof nahi, koi confusing derivation nahi. Bas 5 formulas, kuch standard numbers (coin, die, cards), aur seedhi ginti. Jo student outcome counting mein careful rehta hai, woh is chapter se board exam mein poore marks le jaata hai. Yahan NCERT-level accurate notes — definition, terms, formulas, 2 solved examples aur board ki aam galtiyan — sab kuch simple Roman Hinglish mein.
Prayikta Ki Definition (NCERT Ke Anusaar)
Prayikta (Probability) kisi random experiment mein kisi event ke hone ya na hone ki sambhavna ka numerical maap hai. NCERT ke anusaar, jab experiment ke sabhi possible outcomes equally likely (barabar sambhav) hon, to event E ki probability is formula se nikalti hai:
P(E) = n(E) / n(S) = Favourable outcomes / Total possible outcomes
Yahan n(E) us event ke favourable outcomes ki sankhya hai, aur n(S) sample space ke kul outcomes ki sankhya hai.
Important Terms — Pehle Yeh Samjho
- Random Experiment: Woh experiment jiska result pehle se pata na ho — jaise sikka uchhalna ya pasa phenkna.
- Outcome: Experiment ka ek sambhav result — jaise sikke par Head (H) ya Tail (T).
- Event (E): Sample space ka koi subset — jaise “pase par even number aana” event {2, 4, 6} hai.
- Equally Likely Outcomes: Woh outcomes jinke hone ke chances bilkul barabar hon. Yeh condition bahut zaroori hai — upar wali formula sirf equally likely outcomes par lagti hai.
- Complementary Event (not E): Woh event jismein E hota hi nahi — jaise “Head aana” ka complement “Tail aana” hai.
5 Formulas Jo Exam Mein Seedha Pooche Jaate Hain
- P(E) = Favourable outcomes / Total equally likely outcomes — chapter ka main formula.
- 0 ≤ P(E) ≤ 1 — kisi bhi event ki probability 0 se 1 ke beech hoti hai. Answer is range ke bahar aaye to calculation galat hai.
- P(sure event) = 1 — jo event pakka hoga, uski probability 1 (jaise pase par 1 se 6 ke beech ka number aana).
- P(impossible event) = 0 — jo kabhi ho hi nahi sakta, uski probability 0 (jaise pase par 7 aana).
- P(E) + P(not E) = 1 — isliye P(not E) = 1 − P(E). “Nahi hone” wale sawalon mein yeh formula time bachata hai.
Standard Objects — Coin, Dice, Cards (Yeh Numbers Yaad Kar Lo)
Board exam ke adhiktar sawal inhi teen objects par based hote hain. Inke numbers rat lo:
Sikka (Coin)
- Ek sikka: 2 outcomes — {H, T}
- Do sikke: 4 outcomes — {HH, HT, TH, TT}
- Teen sikke: 8 outcomes — {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
Pasa (Die)
- Ek pasa: 6 outcomes — {1, 2, 3, 4, 5, 6}
- Do pase: 36 outcomes (6 × 6) — ordered pairs jaise (1,1), (1,2)… (6,6). Yeh sabse zyada galat ginne wala number hai — kuch students 12 likh dete hain aur mark kat jaata hai.
- Pase par prime numbers: 3 (2, 3, 5); even numbers: 3 (2, 4, 6); odd numbers: 3 (1, 3, 5)
Tash Ke Patte (Deck of 52 Cards)
- Kul patte: 52 | Red: 26 | Black: 26
- 4 suits (har suit mein 13 patte): Hearts, Diamonds (red), Spades, Clubs (black)
- Face cards: 12 (har suit mein King, Queen, Jack — 4 × 3)
- Aces: 4 | Kings: 4 | Queens: 4 | Jacks: 4
2 Solved Examples (Step-by-Step)
Example 1 — Pasa (Die)
Sawal: Ek pasa ek baar phenka gaya. Prime number aane ki probability kya hai?
Hal:
- Step 1: Total equally likely outcomes n(S) = 6 → {1, 2, 3, 4, 5, 6}
- Step 2: Favourable outcomes (prime numbers) = {2, 3, 5} → n(E) = 3
- Step 3: P(prime number) = 3/6 = 1/2
Example 2 — Do Sikke (Two Coins)
Sawal: Do sikke ek saath uchhale gaye. Exactly one head aane ki probability nikalo.
Hal:
- Step 1: Sample space = {HH, HT, TH, TT} → n(S) = 4
- Step 2: “Exactly one head” wale outcomes = {HT, TH} → n(E) = 2. Dhyaan do — HH mein do heads hain, isliye woh count nahi hoga.
- Step 3: P(exactly one head) = 2/4 = 1/2
Ek aur quick example cards se: 52 patton mein se face card nikalne ki probability = 12/52 = 3/13. Hamesha fraction ko lowest terms tak simplify karna mat bhoolo.
Board Exam Mein 5 Aam Galtiyan (Inse Bachein)
- Total outcomes galat gine — do pase phenkne par 36 outcomes hote hain, 12 nahi. Har baar sample space likhne ki aadat dalo.
- Equally likely condition bhoolna — formula tabhi lagao jab sab outcomes equally likely hon; warna pehle yeh justify karo.
- Favourable outcomes double-count karna — “exactly one head” mein HH include kar lena common mistake hai.
- Fraction simplify na karna — 3/6 likhkar chhod diya, jabki 1/2 expected tha. Aakhiri step mein hamesha simplify karo.
- Range check na karna — answer 1 se zyada ya 0 se kam aaye to calculation mein kahin galti hai; wapas check karo.
Ek Nazar Mein Revision (Exam Se Pehle)
| Point | Yaad Rakho |
|---|---|
| Main formula | P(E) = favourable / total |
| Range | 0 ≤ P(E) ≤ 1 |
| Sure event | P = 1 |
| Impossible event | P = 0 |
| Complement | P(not E) = 1 − P(E) |
| 1 sikka / 1 pasa / 1 deck | 2 / 6 / 52 outcomes |
| 2 sikke / 2 pase | 4 / 36 outcomes |
| Face cards | 12, Red cards 26 |
Prayikta Class 10 Notes — FAQs
Q1. Prayikta chapter Class 10 board mein kitne marks ka aata hai?
Aam taur par is chapter se 2 se 5 marks ke sawal aate hain — coin, die aur cards par based objective aur short questions. Chhota chapter hai, lekin poore marks wala.
Q2. Kya Probability Class 10 mein sirf classical probability padhni hai?
Haan. NCERT Class 10 Chapter 13 mein sirf classical (theoretical) probability hai — experimental probability Class 9 mein thi. Yahan har sawal equally likely outcomes ki assumption par banta hai.
Q3. Do pase wale sawalon mein ordered pairs kyun likhte hain?
Kyunki (2,5) aur (5,2) alag outcomes hain — pehla pasa 2, doosra 5 ya ulta. Agar inhe alag na ginein to total 36 ki jagah kam ho jayega aur probability galat niklegi.
Q4. Probability ke answer ko percentage mein likh sakte hain?
Fraction ya decimal mein likhna sabse safe hai. Percentage tabhi likhein jab sawal mein maanga gaya ho — 1/2 = 0.5 = 50%, teeno sahi hain lekin board mein fraction preferred hai.
Aur Class 10 Maths ke chapter-wise notes ke liye Students section dekhte rahein. Notes NCERT Class 10 Mathematics book par based hain — book ka latest edition ncert.nic.in par verify kar lein.