# IB Maths SL 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:

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

How can we find the probability P(X=2) when

Solution

Using GDC Casio fx-9860G SD

Setting Data: Variable

x: 2

Numtrial:5

p: 0.3

Execute

We find that the probability is

2. IB Mathematics SL – Discrete Probability Distribution, Binomial Distribution

How can we find the probability P(X\geq 2) when

Solution

Using GDC Casio fx-9860G SD

Setting Data: Variable

x: 2

Numtrial:7

p: 0.2

Execute

We find the probability

Therefore