# IB Maths HL 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 () 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:

**Q**uestions and **A**nswers

### 1. IB Mathematics HL – Discrete Probability Distribution, Binomial Distribution

How can we find the probability P(X=3) when

Solution

IB Mathematics HL – Discrete Probability Distribution, Binomial Distribution

Using GDC Casio fx-9860G SD

*MAIN MENU > STAT>DIST(F5)>BINM>Bpd>*

*Setting Data: Variable*

* x: 3*

* Numtrial:3*

* p: 0.3*

*Execute*

We find that the probability is

### 2. IB Mathematics HL – Discrete Probability Distribution, Binomial Distribution

How can we find the probability P(X\geq 3) when

Solution

IB Mathematics HL – Discrete Probability Distribution, Binomial Distribution

Using GDC Casio fx-9860G SD

*MAIN MENU > STAT>DIST(F5)>BINM>Bcd>*

*Setting Data: Variable*

* x: 2*

* Numtrial:7*

* p: 0.2*

*Execute*

We find the probability

Therefore,