Probability and Combinatorics Quiz

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10 Questions

What is the probability of drawing two red cards from a pack of cards?

188/663

In a box containing 4 white, 6 red, 5 black, and 5 other colored balls, what is the probability of drawing either two white balls or two red balls?

21/190

If P(A) = 2/3, P(A' ∩ B) = 1/6, and P(A ∩ B) = 1/3, find P(B).

1/2

What is the probability that there will be no misprint in the page?

1

What is the probability that there will be 1 misprint in the page?

0

What is the probability that there will be at the most 2 misprints?

1

What is the probability density function for the flight time random variable?

1 f(x) = {20 for 120 ≤ x ≤ 140 0 for elsewhere

What is the expected value (mean) of the binomial distribution with n = 20 and p = 0.35?

7

Calculate the variance of the binomial distribution with n = 20 and p = 0.35.

4.55

What is the probability of getting exactly 4 heads when an unbiased coin is tossed 6 times?

15/64

Study Notes

Probability of Drawing Cards and Balls

  • The probability of drawing two red cards from a pack of cards is not specified, but it depends on the number of red cards in the pack.
  • In a box containing 4 white, 6 red, 5 black, and 5 other colored balls, the probability of drawing either two white balls or two red balls can be calculated using the probability of each event.

Conditional Probability

  • If P(A) = 2/3, P(A' ∩ B) = 1/6, and P(A ∩ B) = 1/3, then P(B) can be calculated using the formulas for conditional probability.

Probability of Misprints

  • The probability that there will be no misprint in a page is not specified, but it depends on the probability of a misprint occurring.
  • The probability that there will be 1 misprint in a page is also not specified, but it depends on the probability of a misprint occurring and the number of pages.
  • The probability that there will be at most 2 misprints is not specified, but it depends on the probability of a misprint occurring and the number of pages.

Probability Density Function

  • The probability density function for the flight time random variable is not specified, but it depends on the distribution of the flight time.

Binomial Distribution

  • The expected value (mean) of the binomial distribution with n = 20 and p = 0.35 is np = 20 × 0.35 = 7.
  • The variance of the binomial distribution with n = 20 and p = 0.35 is np(1-p) = 20 × 0.35 × 0.65 = 4.55.

Coin Tossing

  • The probability of getting exactly 4 heads when an unbiased coin is tossed 6 times is 6C4 × (1/2)^4 × (1/2)^2 = 15/64.

Test your knowledge of probability and combinatorics with this quiz. Questions cover topics such as probability calculations, set operations, and card draws. Get ready to challenge yourself with a variety of probability problems.

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