Class 12 Probability · Case Study4 Marksbayes_theorem
Class 12 Maths · Probability · Case Study #132
A shop sells a mixture of flower seeds of types A₁,A₂,A₃ in proportions4:4:2. Their germination probabilities are0.45,0.60,0.35. A seed is selected uniformly from the mixture.
Part (1) 2 Marks
Find P(the seed germinates).
Answer: 49/100
- The type probabilities are4/10,4/10,2/10. Apply total probability.
- P(G)=(4/10)(45/100)+(4/10)(60/100)+(2/10)(35/100)=0.18+0.24+0.07.
- Thus P(G)=0.49=49/100.
Part (2) 2 Marks
Given germination, find P(type A₂).
Answer: 24/49
- Bayes gives P(A₂|G)=P(A₂)P(G|A₂)/P(G).
- The numerator is(4/10)(60/100)=0.24, and P(G)=0.49.
- Thus P(A₂|G)=0.24/0.49=24/49.