Consider a deck of cards. Suppose we are drawing ten cards with replacement. What is the probabilityof finding at least 4 face cards?
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.
Consider a deck of cards. Suppose we are drawing ten cards with replacement. What is the probabilityof finding at least 4 face cards?
A deck of cards contains 52 cards. 12 cards are face cards.
Since 10 cards are drawn with replacement, then the probability of selecting a card every time is equal.
The probability of selecting a face card is
Suppose, X be the number of face cards drawn out of 10 draws.
Then X follows Binomial distribution with parametres
Hence, the probability mass function is
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