A sample of two balls is chosen at random from a box containing 5 white and 5 black balls, and we denote by X the number of black balls in the sample. (a) Give the probability mass function of X. (b) If two more balls are chosen from the remaining 8 balls, what is the probability that these two additional balls are black? (c) What is the conditional probability that the two balls from the first sample were white given that the two balls from the second sample are black?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Statistics and Probability
3. A sample of two balls is chosen at random from a box containing 5 white and 5 black balls, and we denote by X the number of black balls in the sample.
(a) Give the probability mass
(b) If two more balls are chosen from the remaining 8 balls, what is the probability that these two additional balls are black?
(c) What is the conditional probability that the two balls from the first sample were white given that the two balls from the second sample are black?
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