Binomial problems: Basic Suppose that the New England Colonials baseball team is equally likely to win a game as not to win it. If 4 Colonials games are chosen at random, what is the probability that exactly 3 of those games are won by the Colonials? Round your response to at least three decimal places. (If necessary, consult a list of formulas.) Explanation Check
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.
Given Information :
Suppose that the New England Colonials baseball team is equally likely to win a game as not to win it. 4 Colonials games are chosen at random.
Let, p denotes probability of winning a game .
p = 0.5 (equally likely)
n denotes sample size
n = 4
Define random variable X denotes number of games are won by colonials .
Since , events are independent . X ~ B (n=4,p=0.5)
Binomial Probability formula is given as :
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