Binomial Distribution Calculator

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Example

Created on 2024-06-20Asked by Oliver Smith (Solvelet student)

Find the probability of getting exactly 4 heads in 10 flips of a fair coin.

Solution

Step 1: Identify the parameters for the binomial distribution. Here,

n = 10

k = 4

, and

p = 0.5

. Step 2: Use the binomial probability formula:

P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}.

Step 3: Substitute

n = 10

k = 4

, and

p = 0.5

into the formula:

P(X = 4) = \binom{10}{4} (0.5)^4 (0.5)^{10-4} = \binom{10}{4} (0.5)^{10}.

Step 4: Calculate the binomial coefficient:

\binom{10}{4} = \frac{10!}{4!(10-4)!} = \frac{10!}{4!6!} = 210.

Step 5: Calculate the probability:

P(X = 4) = 210 \cdot (0.5)^{10} = 210 \cdot \frac{1}{1024} = \frac{210}{1024} = 0.205.

Step 6: Conclusion. The probability of getting exactly 4 heads in 10 flips of a fair coin is 0.205. Solved on Solvelet with Basic AI Model

Some of the related questions asked by Madison Hernandez on Solvelet

1. Calculate the probability of a fair coin getting exactly 3 heads in 5 flips 2. Find the mean and standard deviation of the binomial distribution with parameters

n = 10

and

p = 0.3

DefinitionBinomial distribution is defined as “a discrete probability distribution that applies the probability of a given number of successes in a fixed number of independent Bernoulli trials—trials that are identical in nature and for which the probability of success stays the same”. It is defined with respect to two parameters, n and p, where n is the number of trials and p is the probability of success. In statistics, statistics, probability theory, and experimental design, there are many situations where a set number of outcomes is available. For instance, tossing a fair-coin results in finding the occurrence of heads with the binomial distribution, b(10, 0.5).

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