What is the Probability (?)

Question

1. Find C(n, x)p^xq^n − x for the given values of n, x, and p. (Round your answer to four decimal places.) n=9, x=6, p=1/4
2. Find C(n, x)p^xq^n − x for the given values of n, x, and p. (Round your answer to four decimal places.) n=7, x=4, p= 0.2

Use the formula C(n, x)p^xq^n − x to determine the probability of the given event. (Round your answer to four decimal places.) The probability of exactly five successes in ten trials of a binomial experiment in which p= 1/2

Answer 1

In Probability, these are terms from the polynomial of nth degree where p+q =1.

(1)C(n, x)p^xq^n − x

Given: n=9, x=6, p=1/4

Since p+q =1

∴ q = 3/4

Substitute:

C(n, x)p^xq^n − x = C(9,6) (1/4)⁶ (3/4)^9-6 = 84• (1/4)⁶ (3/4)³

≈ 0.0087

(1)Find C(n, x)p^xq^n − x

Given:  n=7, x=4, p= 0.2

∴ q = 0.8

Substitute:

C(n, x)p^xq^n − x = C(7, 4)(0.2)⁴(0.8)^7 − 4 = 35•(0.2)⁴(0.8)³

≈0.0287

For the last problem:

n = number of trials = 10

p = probability = 1/2

x = successes = 5

q = 1-p

It's exactly five success therefore we can use the formula:

C(n, x)p^xq^n − x

= C(10,5) (1/2)⁵ (1/2)⁵

≈0.2461