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Probability and Combinatorics Quiz

Probability and Combinatorics: ten questions on counting, conditional probability, and expected-value calculations. Every answer is explained.

Free, with no sign-up.

ByLelfy Editorial Team

For High school students and adults reviewing the topic.

About 13 minutes. 10 questions.

How does it work?

  1. Choose one answer or enter a number as requested, then check it.
  2. Read the explanation before continuing.
  3. Round only the final answer to the precision requested.

What will you get?

See your score and review the reasoning behind each answer.

Question 1Seven finalists compete for a distinct first and second place. How many ordered outcomes are possible? Enter a whole number.

Answers within 0.5 of the expected value are accepted.

Question 2From nine volunteers, a team of four is selected with no assigned roles. How many teams are possible? Enter a whole number.

Answers within 0.5 of the expected value are accepted.

Question 3A bag has 7 green and 13 white tokens, each equally likely to be drawn. Find the probability of green, rounded to two decimals.

Answers within 0.005 of the expected value are accepted.

Question 4A model assigns probability 0.18 to a delivery being late. Find the probability it is not late, rounded to two decimals.

Answers within 0.005 of the expected value are accepted.

Question 5Inspection records show Line A: 36 pass and 4 fail; Line B: 24 pass and 6 fail. Given that a part failed, find the probability it came from B, rounded to two decimals.

Answers within 0.005 of the expected value are accepted.

Question 6A random payout is $18 with probability 0.2 and $3 with probability 0.8. Find its expected value in dollars to the nearest cent.

Answers within 0.005 dollars of the expected value are accepted.

Question 7On a panel, a chair and a recorder have distinct duties. What changes when the two people swap roles?
Question 8One fair die is rolled. Which description fits the events “result 1” and “result 6”?
Question 9Two independent components each work with probability 0.9. What is the probability both work?
Question 10A fair coin has shown tails in four independent tosses. What is the probability of heads on the next toss?

Answer every question to see and share your score.

Read the topic guide