Suppose that we perform an experiment where we classify the outcome as either a success or a failure. Let the probability of a success be 0.90.9 . Now we want to repeat this experiment n = 44 times and let the random variable X count the number of successes. Visualize a probability tree for this situation (without actually drawing it out). Round to four decimal places as needed. From each vertex there will be 22 edges going to a success S and a failure F. Since each stage is independent all the edges going to an S will have probability p = . 9.9 and all the edges going to an F will have probability q = . 10.10. If a single path has 2 success and the rest failures (in any order) then the probability of that single path is nothing. Note that these 2 successes may be in any of the 44 stages so there are nothingof these paths which have 2 successes. Therefore, P(X = 2) = nothing.
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.
Suppose that we perform an experiment where we classify the outcome as either a success or a failure. Let the
0.9
0.9 . Now we want to repeat this experiment n =
4
4 times and let the random variable X count the number of successes. Visualize a probability tree for this situation (without actually drawing it out). Round to four decimal places as needed.
From each vertex there will be
2
2 edges going to a success S and a failure F. Since each stage is independent all the edges going to an S will have probability p =
. 9
.9 and all the edges going to an F will have probability q =
. 10
.10.
If a single path has 2 success and the rest failures (in any order) then the probability of that single path is
nothing
.
Note that these 2 successes may be in any of the
4
4 stages so there are
nothing
of these paths which have 2 successes.
Therefore, P(X = 2) =
nothing
.
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 2 images
