## Binomial Distribution

Discussions for the Core part of the syllabus. Algebra, Functions and equations, Circular functions and trigonometry, Vectors, Statistics and probability, Calculus. IB Maths HL Revision Notes

### Binomial Distribution

Discrete Probability Distribution, Binomial Distribution - IB Maths HL

How can we find the probability $P(X=5)$ when $X\sim B(12,0.2)$

Thanks
lora

Posts: 0
Joined: Wed Apr 10, 2013 7:36 pm

### Re: Binomial Distribution

IB Mathematics HL – Discrete Probability Distribution, Binomial Distribution

The Binomial distribution can be used in situations in which a given experiment (trial) is repeated a number of times. For the binomial model to be applied the following four criteria must be satisfied
- the trial is carried out a fixed number of times $n$.
- the outcomes of each trial can be classified into two ‘types’ conveniently named success or failure.
- the probability $p$ of success remains constant for each trial.
- the individual trials are independent of each other.

If a discrete random variable X follows a binomial distribution ($X\sim B(n,p)$) with $n$ is the number of trials and $p$ the probability of a success, then the probability distribution function is given by the following formula:

$P(X=x)= \displaystyle \binom{n}{x} p^x (1-p)^{n-x}, x=0,1,2,…,n$

Therefore,

$P(X=5)= \displaystyle \binom{12}{5} (0.2)^5 (0.8)^{12-5}=0.05315$

Using GDC Casio fx-9860G SD

Setting Data: Variable
x :5
Numtrial:12
p :0.2
Execute

We find that the probability is
$P(X=3)= 0.05315$

Hope these help!!
lily

Posts: 0
Joined: Mon Jan 28, 2013 8:04 pm

### Re: Binomial Distribution

Thanks Lily!!
lora

Posts: 0
Joined: Wed Apr 10, 2013 7:36 pm