Q. Two cards are drawn at random from a pack of 52 cards. What is the probability that both are of different suits?

  • (A) 13/17
  • (B) 4/17
  • (C) 26/51
  • (D) 25/51
πŸ“ Notes
βœ… Correct Answer: (A) 13/17
Explanation: Complement of same suit. Probability = 1 - 4/17 = 13/17.

Q. Two cards are drawn at random from a pack of 52 cards. What is the probability that at least one card is red?

  • (A) 77/102
  • (B) 25/102
  • (C) 26/51
  • (D) 4/17
πŸ“ Notes
βœ… Correct Answer: (A) 77/102
Explanation: Complement: both black = 26C2/52C2 = 25/102. Required probability = 1 - 25/102 = 77/102.

Q. Two cards are drawn at random from a pack of 52 cards. What is the probability that both are Jacks?

  • (A) 1/221
  • (B) 2/221
  • (C) 4/221
  • (D) 6/221
πŸ“ Notes
βœ… Correct Answer: (A) 1/221
Explanation: There are 4 Jacks. Probability = 4C2/52C2 = 6/1326 = 1/221.

Q. Two cards are drawn at random from a pack of 52 cards. What is the probability that neither card is a King?

  • (A) 188/221
  • (B) 33/221
  • (C) 32/221
  • (D) 130/221
πŸ“ Notes
βœ… Correct Answer: (A) 188/221
Explanation: Non-Kings = 48. Probability = 48C2/52C2 = 1128/1326 = 188/221.

Q. Two cards are drawn at random from a pack of 52 cards. What is the probability that exactly one card is a King?

  • (A) 32/221
  • (B) 33/221
  • (C) 16/221
  • (D) 1/221
πŸ“ Notes
βœ… Correct Answer: (A) 32/221
Explanation: Favorable ways = 4 × 48 = 192. Probability = 192/1326 = 32/221.

Q. Two cards are drawn at random from a pack of 52 cards. What is the probability that at least one card is black?

  • (A) 77/102
  • (B) 25/102
  • (C) 26/51
  • (D) 13/17
πŸ“ Notes
βœ… Correct Answer: (A) 77/102
Explanation: Complement: both red = 26C2/52C2 = 25/102. Required probability = 1 - 25/102 = 77/102.

Q. Two cards are drawn at random from a pack of 52 cards. What is the probability that one card is a Heart and the other is a Spade?

  • (A) 26/221
  • (B) 13/221
  • (C) 52/221
  • (D) 1/17
πŸ“ Notes
βœ… Correct Answer: (A) 26/221
Explanation: Favorable ways = 13 × 13 = 169. Probability = 169/1326 = 26/221.

Q. Two cards are drawn at random from a pack of 52 cards. What is the probability that both are Hearts?

  • (A) 1/17
  • (B) 4/17
  • (C) 13/52
  • (D) 25/102
πŸ“ Notes
βœ… Correct Answer: (A) 1/17
Explanation: There are 13 Hearts. Probability = 13C2/52C2 = 78/1326 = 1/17.

Q. A can complete a work in 12 days and B can complete the same work in 18 days. In how many days can they complete the work together?

  • (A) 7.2 days
  • (B) 8 days
  • (C) 9 days
  • (D) 10 days
πŸ“ Notes
βœ… Correct Answer: (A) 7.2 days
Explanation: A's one-day work = 1/12, B's one-day work = 1/18. Together = 5/36. Time = 36/5 = 7.2 days.

Q. A can complete 1/4 of a work in 5 days. In how many days will A complete the whole work?

  • (A) 15 days
  • (B) 20 days
  • (C) 25 days
  • (D) 30 days
πŸ“ Notes
βœ… Correct Answer: (B) 20 days
Explanation: If 1/4 work takes 5 days, the whole work takes 5 × 4 = 20 days.

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