Class 12 Probability · Long Answer3 Marksindependence
Class 12 Maths · Probability · Long Answer #106
Students A,B arrive on time independently with probabilities 3/7,5/7. Find P(exactly one is on time).
✅ Step-by-Step Solution
Final Answer: 26/49
- The favorable disjoint events are A on time,B late and A late,B on time.
- By independence their probabilities are (3/7)(2/7)=6/49 and (4/7)(5/7)=20/49.
- Add the disjoint probabilities: 6/49+20/49=26/49.
- Therefore P(exactly one is on time)=26/49.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] The favorable disjoint events are A on time,B late and A late,B on time.
- [1 mark] By independence their probabilities are (3/7)(2/7)=6/49 and (4/7)(5/7)=20/49.
- [1 mark] Add the disjoint probabilities: 6/49+20/49=26/49.
- [0.5 marks] Therefore P(exactly one is on time)=26/49.
Master Chapter 13: Probability
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Probability.
← Previous Question
Choose bags X,Y with equal probability. X contains4 white,2 black; Y…
Next Question →A,B independently fire once at a target with hit probabilities…
More Practice Questions in Probability
Related Questions in Probability
Class 12 Probability · Mcq Single Correct
Given P(A)=4/5 and P(A∩B)=7/10, find P(B|A).
Class 12 Probability · Mcq Single Correct
Five independent fair coins are tossed. Find the probability of at least one head.
Class 12 Probability · Mcq Single Correct
Given P(A|B)=0.3, P(A)=0.4, P(B)=0.8, find P(B|A).
Class 12 Probability · Mcq Single Correct
Two independent fair dice have sum 9. Find the conditional probability that at least one die…
Class 12 Probability · Mcq Single Correct
Choose an ordered pair (a,b) uniformly with distinct a,b from {1,2,3,4,5}. Find P(a/b is an…
Class 12 Probability · Mcq Single Correct
Given P(A)=0.4, P(B)=0.3 and P(A∪B)=0.5, find P(B′∩A).