Explanation
1. Di gayi Values (Given Data)
Dono bags me se kisi ek ko chunne ki probability barabar hogi:
Ab, har bag se Red ball nikalne ki probability:
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Bag A se Red (3 Red, 4 Black): P(A∣E1)=73
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Bag B se Red (5 Red, 6 Black): P(A∣E2)=115
2. Bayes' Theorem ka Formula
Humein nikalna hai P(E2∣A), yani ki probability ki bag B tha agar ball red nikli:
P(E2∣A)=P(E1)⋅P(A∣E1)+P(E2)⋅P(A∣E2)P(E2)⋅P(A∣E2)
3. Calculation
Values ko formula mein rakhte hain:
P(E2∣A)=(21×73)+(21×115)21×115
21 common lekar cancel ho jayega:
Denominator ka LCM (7×11=77) lene par:
P(E2∣A)=7733+35115=115×6877
Answer:
Bag B se ball nikalne ki probability 35/68 hai.
