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.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
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.
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).
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.
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.
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.