Consider a binomial experiment with n = 4 trials where the probability of success on a single trial is p = 0.25. (For each answer, enter a number. Round your answers to three decimal places.) (a) Find P(r = 0). (b) Find P(r ≥ 1) by using the complement rule.

In binomial experiment with 4 trials, Probabilities shown below.

               and  

The Probability of r number of successes in n trials is given by a binomial expression,

Where p represent probability of success and q represent probability of unsuccessful.

Number of trials, n = 4

Probability of success, p = 0.25  and  q = 1 - 0.25 = 0.75

Learn more about binomial expression here :

link

(a) 0.32

(b) 0.68

Step-by-step explanation:

It is given that a binomial experiment is carried out.

n = 4 trials

Probability of success, p = 0.25

We know that in a binomial experiment:

Probability of success + Probability of failure = 1

p + q = 1

So, q = 1 - 0.25 = 0.75

Probability of 'r' number of successes in 'n' trials of a binomial experiment is given as:

(a) P(r = 0) = ?

Putting values of x = 0, p and q:

(b) Find P(r ≥ 1)  = ?

Using complement rule:

P(r =0 ) + P(r ≥ 1)  = 1

0.32 + P(r ≥ 1)  = 1

P(r ≥ 1)  = 1 - 0.32

P(r ≥ 1)  = 0.68

So, the answer are:

(a) 0.32

(b) 0.68

i hope this is what you were looking for.

see attached graph

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for