English
Menu

Probability, Statistics and Queueing

Among 10 lottery tickets, 3 are winners. Two tickets are drawn one after the other, and a drawn ticket is not put back. Which of the following is the probability that both are winners?

  1. A1/45
  2. B1/15
  3. C9/100
Show answer and explanation

Answer: B. 1/15

The probability that the first ticket wins is 3/10. Given that the first ticket won, 2 of the remaining 9 tickets are winners, so the conditional probability that the second ticket wins is 2/9. The probability that both win is therefore 3/10 × 2/9 = 6/90 = 1/15. Thinking in combinations, dividing the 3C2 = 3 ways of choosing 2 of the 3 winners by the 10C2 = 45 ways of choosing 2 of the 10 tickets also gives 3/45 = 1/15.

  • A. This counts only one pair of winners among the 45 ways of choosing 2 of the 10 tickets. There are 3 ways to choose 2 of the 3 winners.
  • B. Correct. 3/10 × 2/9 = 1/15.
  • C. This is (3/10)² = 9/100, the result when the drawn ticket is put back. Without putting it back, the probability that the second ticket wins changes to 2/9.
Practice this topic Back to topic

Related calculators

Queueing calculator (M/M/1 and M/M/c)Utilization, mean waiting time, response time and queue length for M/M/1 and M/M/c from the arrival rate, mean service time and number of servers

Books on Probability, Statistics and Queueing Ad

As an Amazon Associate I earn from qualifying purchases.

More Probability, Statistics and Queueing questions

  1. A fab processed 500 wafers in a month, 100 of them in chamber 2. A total of 40 wafers failed, and 15 of these had been processed in chamber 2. Which of the following is the conditional probability that a wafer processed in chamber 2 fails?
  2. In a population of chips, 1% have a latent defect. A screening test judges 95% of the defective chips positive and wrongly judges 4% of the good chips positive. Which of the following is closest to the probability that a chip judged positive is actually defective?
  3. There are 1,000 lottery tickets at ¥50 each: one wins a ¥10,000 prize, ten win ¥1,000 prizes, and the rest win nothing. Which of the following is the expected value of the prize per ticket?
  4. A chip costs ¥300 to make. A good chip sells for ¥500, and a defective chip cannot be sold and is discarded. If the probability that a chip is good is 80%, which of the following is the expected profit per chip made?
  5. Ten keys are stored in a hash table with 100 buckets. Each key is assigned independently to one of the 100 buckets with equal probability. Which of the following is the expected number of pairs of keys that are assigned to the same bucket?