Class 12 Probability · Case Study4 Marksconditional_probability
Class 12 Maths · Probability · Case Study #130
A,B,C are three activity types. The Venn model has disjoint-region probabilities: A only0.32; A∩B0.09; B only y; B∩C x; C only0.21; outside all0.11. A∩C=∅, so the triple intersection is empty. Given P(C)=0.44, answer the following.
Part (1) 1 Marks
Find x.
Answer: x=0.23
- C consists of its only-region and B∩C, so P(C)=0.21+x.
- Thus x=0.44−0.21=0.23.
Part (2) 1 Marks
Find y.
Answer: y=0.04
- All six disjoint regions sum to1.
- Thus y=1−(0.32+0.09+0.23+0.21+0.11)=0.04.
Part (3) 2 Marks
Find P(C|B).
Answer: 23/36
- P(C|B)=P(B∩C)/P(B).
- Here P(B∩C)=0.23 and P(B)=0.09+0.04+0.23=0.36.
- Therefore P(C|B)=0.23/0.36=23/36.
Part (4) 2 Marks
Find P((A∪B)∩C′).
Answer: 0.45
- The required disjoint regions are A only,A∩B,and B only.
- Add their masses:0.32+0.09+0.04=0.45.
- Thus P((A∪B)∩C′)=0.45.