14.2 Theoretical Probability (Classical Definition)

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Key Formulas

Solved Examples

Step 1

  1. Analyze Sample Space: Total balls = 3 (Red, Blue, Yellow). Total outcomes = 3. Since balls are identical in size, picking any one is equally likely.

Step 2

  1. (i) Yellow Ball: Let Y be the event 'the ball taken out is yellow'. The number of outcomes favorable to Y is 1. P(Y)=13P(Y) = \frac{1}{3}

Step 3

  1. (ii) Red Ball: Let R be the event 'the ball taken out is red'. The number of outcomes favorable to R is 1. P(R)=13P(R) = \frac{1}{3}

Step 4

  1. (iii) Blue Ball: Let B be the event 'the ball taken out is blue'. Favorable outcomes = 1. P(B)=13P(B) = \frac{1}{3}

Step 5

  1. Verification: Sum of probabilities = 1/3+1/3+1/3=11/3 + 1/3 + 1/3 = 1. This confirms that these are the only elementary events.
Final Answer

(i) 1/3, (ii) 1/3, (iii) 1/3

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