BBBASICSTAT8 6.2.501.XP

Question

In the binomial probability distribution, let the number of trials be n = 3, and let the probability of success be p = 0.4012. Use a calculator to compute the following.

(a) The probability of two successes. (Round your answer to three decimal places.)

(b) The probability of three successes. (Round your answer to three decimal places.)

(c) The probability of two or three successes. (Round your answer to three decimal places.)

Answer 1

For binary distribution, the probability density function is as follows. (use link to see formula in wikipedia)

https://en.wikipedia.org/wiki/Binomial_distribution

So - Q1. n = 3 p = .4012 k = 2. (3!/(2!*1!) * .4012²*(1-.4012) = .289

Q2 = n = 3 p = .4012 k = 3. (3!/(3!*0!) * .4012³*(1-.4012)⁰ = 0.065

Q3 = P(X=3) + P(X=2) = 0.354

Or you could use the binary distribution calculator in the Ti-86, or the dbinom() function in R