Binomial
An algebraic expression with two terms
The binomial is a type of probability distribution that describes the number of successful outcomes in a fixed number of trials where there are only two possible outcomes (success or failure). It is used in many fields of study, such as statistics, economics, and genetics.
The binomial formula is:
P(X=k) = (n choose k) * p^k * (1-p)^(n-k)
Where:
– P(X=k) is the probability of getting k successes in n trials
– n is the total number of trials
– k is the number of successful outcomes
– p is the probability of a success on any one trial
– (n choose k) represents the number of ways k successful outcomes can be achieved in n trials
We can use the binomial distribution to answer questions such as: What is the probability of getting exactly 4 heads in 10 coin flips, if the probability of getting heads on each flip is 0.5?
To solve this problem, we use the binomial formula as follows:
P(X=4) = (10 choose 4) * 0.5^4 * 0.5^6
P(X=4) = 0.205
Therefore, the probability of getting exactly 4 heads in 10 coin flips, if the probability of getting heads on each flip is 0.5, is 0.205.
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