# Calculate P(x > 2): Binomial Distribution

• nachelle
For the first case, n= 8, p= 0.3, P(x= m)= 8Cm(0.3)m(0.7)8-m, m= 0, 1, 2. For the second, n= 6, p= 0.1, P(x= m)= 6Cm(0.1)m(0.9)6-m, m= 0, 1, 2.In summary, when given a discrete, binomial random variable x and the number of trials (n) and success probability (p), we can calculate the probability of x being greater than 2 by either finding the probability of x being equal to
nachelle
Suppose x is a discrete, binomial random variable

Calculate P(x > 2), given trails n = 8, success probability p = 0.3

and

given trails n = 6, success probability p = 0.1

When it says n is more than 2, it means that x = 3, 4, and so on until 8. You can compute the probabilities for each of the values of x wanted, or you can find the answer by applying the formula and using the statistical tables.

nachelle said:
Suppose x is a discrete, binomial random variable

Calculate P(x > 2), given trails n = 8, success probability p = 0.3

and

given trails n = 6, success probability p = 0.1
First, it "trials", not "trails"! P(x= m)= 8Cm(0.3)m(0.7)8-m. Since "x> 2" means x= 3, 4, 5, 6, 7, or 8, it might be simpler to find find P(x<= 2)= P(x= 0)+ P(x=1)+ P(x= 2) and then subtract from 1.

## 1. What is the formula for calculating P(x > 2) in a binomial distribution?

The formula for calculating P(x > 2) in a binomial distribution is 1 - P(x = 0) - P(x = 1) - P(x = 2). This formula takes into account the probability of getting 0, 1, or 2 successes and subtracts it from 1 to get the probability of getting more than 2 successes.

## 2. How do you calculate P(x > 2) if given a specific probability and number of trials?

If given a specific probability and number of trials, you can use the formula 1 - (n choose 0)(p^0)(1-p)^(n-0) - (n choose 1)(p^1)(1-p)^(n-1) - (n choose 2)(p^2)(1-p)^(n-2) to calculate P(x > 2). This formula represents the binomial probability distribution function and takes into account the number of trials (n), probability of success (p), and the number of desired successes (in this case, more than 2).

## 3. What is the difference between P(x > 2) and P(x ≥ 2) in a binomial distribution?

In a binomial distribution, P(x > 2) represents the probability of getting more than 2 successes in a given number of trials, while P(x ≥ 2) represents the probability of getting 2 or more successes. This means that P(x ≥ 2) includes the probability of getting exactly 2 successes, while P(x > 2) does not.

## 4. How does changing the number of trials affect the value of P(x > 2) in a binomial distribution?

As the number of trials increases, the value of P(x > 2) in a binomial distribution decreases. This is because with more trials, the probability of getting more than 2 successes becomes smaller as there are more opportunities for unsuccessful events to occur.

## 5. Can P(x > 2) ever be equal to 1 in a binomial distribution?

No, P(x > 2) can never be equal to 1 in a binomial distribution. This is because the maximum probability for a binomial distribution is 1, and P(x > 2) represents a probability of getting more than 2 successes, which is less than the maximum probability. However, P(x > 2) can approach 1 as the number of trials increases.

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