Question

For a binomial distribution with p(x>2), what is the probability of p(x=3)?

A) Cannot be determined from the given information.
B) p(x=3)=1−p(x≤2)
C) p(x=3)=p(x>2)−p(x>3)
D) p(x=3)=p(x≥3)−p(x>3)

Answer 1

The probability of exactly 3 successes in a binomial distribution, given p(x>2), is found by subtracting the cumulative probability of up to 2 successes from 1. The correct formula is p(x=3) = 1 - p(x≤2).

Step-by-step explanation:

The question asks about the probability of observing a certain number of successes (x=3) in a binomial distribution given the probability of observing more than a certain number (x>2). Option B is the correct answer: p(x=3) = 1 - p(x≤2).

To calculate the probability of exactly 3 successes, you would subtract the cumulative probability up to 2 successes from 1 (the total probability space). So, in general terms, p(x=3) = 1 - p(x≤2), where p(x≤2) includes the probabilities for 0, 1, and 2 successes.

It should not be confused with the Poisson distribution, where p(x=2) ≈ .2653, or with the cumulative probabilities provided by a Poisson distribution (e.g., p(x>2) = 1 - p(x≤2) ≈ .2505).