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

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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