# Thread: New to Binomial and Probability

1. ## New to Binomial and Probability

Hi everyone,

Im new to all this. I have been spending alot of time these past few days doing various things related to Stats etc.

Im trying to understand, but its hard for me and I need help understanding. Here is a question;

Assume a binomial experiment in the following questions. Find the probability;
a) of exactly 5 successes, where n=7 and p=0.5
b) of between 8 and 12 successes, where n=15 and p=0.7
c) of at least 8 successes, where n=12 and p=0.5

Being so new I am having a hard time with this. Any help?

Duey

2. Originally Posted by Duey
Hi everyone,

Im new to all this. I have been spending alot of time these past few days doing various things related to Stats etc.

Im trying to understand, but its hard for me and I need help understanding. Here is a question;

Assume a binomial experiment in the following questions. Find the probability;
a) of exactly 5 successes, where n=7 and p=0.5
b) of between 8 and 12 successes, where n=15 and p=0.7
c) of at least 8 successes, where n=12 and p=0.5

Being so new I am having a hard time with this. Any help?

Duey
for the binomial distribution $B(N,p)$, the probability of exactly $n$ successes from $N$ and individual case probability of success $p$ is:

$
p(n; N, p)=\frac{N!}{n!(N-n)!}p^n(1-p)^{N-n}
$

for part a sunbstitue in the given values.

for part b (assuming it is between 8 and 12 successes inclusive):

$
p(8,15,0.7)+p(9,15,0.7)+p(10,15,0.7)+p(11,15,0.7)+ p(12,15,0.7)
$

for part c:

$
p(8,12,0.5)+p(9,12,0.5)+p(10,12,0.5)+p(11,12,0.5)+ p(12,12,0.5)
$

That is you sum the probabilities for the case3s included by the condition

RonL

3. The trouble im having is doing the actual fomula, some of it i understand, some of it i don't. Looking for step by step instructions to show me so I can actually understand it.

4. Originally Posted by Duey
The trouble im having is doing the actual fomula, some of it i understand, some of it i don't. Looking for step by step instructions to show me so I can actually understand it.
i'll show you how to do the first, the rest are similar:

In the Binomial distribution we have that, the probability of $k$ successes in $n$ trials is given by:

$P(k) = {n \choose k}p^kq^{n-k}$

where $p$ is the probability of success, and $q = 1 - p$ is the probability of failure.

In this question, $n = 7, ~p = q = 0.5$

we want P(5) ...exactly 5 successes

thus, $P(5) = {7 \choose 5} \left( \frac 12 \right)^5 \left( \frac 12 \right)^2 = 21 \cdot \frac 1{32} \cdot \frac 14 = \frac {21}{128}$

for (b), between 8 and 12 successes (inclusive)

we want $P(8 \le k \le 12) = P(8) + P(9) + P(10) + P(11) + P(12)$

find each as i did the one above and sum them. here n = 15, p = 0.7, q = 0.3

for (c), we want the probability of 8 or more successes.

that is, $P(k \ge 8) = P(8) + P(9) + P(10) + P(11) + P(12)$

here, n = 12, p = q = 0.5