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:
Questions and Answers
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,