CBSE Class 12 Mathematics 2026 Supplementary Paper 65(B)/7 · Q355 Marksbayes_theorem
CBSE Class 12 Mathematics 2026 Supplementary Paper 65(B)/7 · Question 35 (Probability)
A uniformly random card is lost from a standard deck. Two cards drawn from the rest are both spades. Find the probability the lost card was a spade. OR Three fair coins are tossed. Let A be three heads or three tails, B at most two heads, and C at least two heads. Test (A,C) and (B,C) for independence.
Alternative 1 5 Marks
A uniformly random card is lost from a standard deck. Two cards drawn from the rest are both spades. Find the probability the lost card was a spade.
Answer: 11/50.
- Regard the lost card and the two draws as three ordered positions in a uniformly shuffled deck.
- Given that the two draw positions are spades, the lost-card position is uniformly filled from the other 50 cards, of which 11 are spades.
- The conditional probability is therefore 11/50.
Alternative 2 5 Marks
Three fair coins are tossed. Let A be three heads or three tails, B at most two heads, and C at least two heads. Test (A,C) and (B,C) for independence.
Answer: (A,C) independent; (B,C) dependent.
- Count eight equally likely outcomes, giving P(A)=1/4, P(B)=7/8 and P(C)=1/2.
- A∩C contains only HHH, giving 1/8=P(A)P(C). B∩C contains the three outcomes with exactly two heads.
- Since 3/8 differs from P(B)P(C)=7/16, B and C are dependent.