Probability and Combinatorics Quiz

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.