English
Menu

Probability, Statistics and Queueing

When a die is rolled 3 times, which of the following is closest to the probability that a 6 comes up at least once?

  1. A0.42
  2. B0.50
  3. C0.58
Show answer and explanation

Answer: A. 0.42

The probability of "at least once" is easily found by subtracting from 1 the probability of its complement, "not even once". The probability of not rolling a 6 in one roll is 5/6, and the 3 rolls are independent, so the probability of no 6 at all is (5/6)³ = 125/216 ≈ 0.58. The required probability is therefore 1 − 125/216 = 91/216 ≈ 0.42.

  • A. Correct. 1 − (5/6)³ = 91/216 ≈ 0.42.
  • B. This adds 1/6 three times. It counts the cases with two or more 6s more than once, so the probabilities cannot simply be added like this.
  • C. (5/6)³ ≈ 0.58 is the probability that no 6 comes up at all.
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. 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?
  2. 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?
  3. 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?
  4. 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?
  5. 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?