NCERT Class 12 · Ch 13 Exercise 13.2 · Q15
NCERT Class 12 Maths · Chapter 13 Probability · Exercise 13.2 Question 15
For one random card, check independence: (i) spade vs ace; (ii) black vs king; (iii) king-or-queen vs queen-or-jack.
💡 Concept Hints
- Define the events and identify which event is being conditioned on.
- Use P(E|F)=P(E∩F)/P(F), or separate the possible sources before applying total probability and Bayes.
✅ Step-by-Step Solution
Final Answer: (i),(ii) independent; (iii) dependent.
- (i) P(spade)=1/4,P(ace)=1/13; their intersection is the ace of spades, 1/52, equal to the product.
- (ii) P(black)=1/2,P(king)=1/13; two black kings give 2/52=1/26, equal to the product.
- (iii) Both marginals are 8/52=2/13, but the intersection is four queens, 1/13≠4/169.
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