Chapter 15 Probability

Notes

Probability

Probability batata hai ki kisi event ke hone ki possibility kitni hai. Probability ka value hamesha 0 se 1 ke beech hota hai.

Important Terms:

Experiment Jaise coin toss karna, die throw karna. Outcome Experiment ka result. Coin toss → Head ya Tail. Event Desired outcome. Example: Head aana. Sample Space (S) Sabhi possible outcomes ka set. Coin toss: {H, T} Die throw: {1, 2, 3, 4, 5, 6} Favourable Outcomes Jo outcomes hume chahiye.

Probability Formula:

P(E)= Total Outcomes Favourable Outcomes ​

Special Cases:

Impossible Event → Probability = 0 Sure Event → Probability = 1

Important Properties:

0 ≤ P(E) ≤ 1 P(Not E) = 1 - P(E)

Standard Examples:

Coin toss: P(Head) = 1/2 P(Tail) = 1/2 Die throw: P(any one number) = 1/6 Deck of cards: Total cards = 52 Red cards = 26 Black cards = 26 Kings = 4 Queens = 4 Aces = 4

Common Mistakes:

Total outcomes galat count karna Favorable outcomes miss kar dena Fraction simplify na karna

Exam Tips:

Pehle sample space likho Favorable outcomes count karo Formula apply karo Answer simplest form me do