Page 49 - Math SL HB Sem 3

Binomial Distribution

- a type of discrete probability distribution

When you have a situation that your experiment can only result in 2 outcomes (e.g. hit or miss; faultless
or faulty; yes or no; male or female) and that at each trial, the probability of success remains the same;
as you repeat this experiment n times, you will obtain a binomial distribution - a discrete probabjlity
distribution.

You can express lhe random variable X for such a case as:

-
X B (n,p) '-' can be read as'(n is
dbtributed as'
where n = the number of trials
p probability of success at each trial
=
Problem-solving flow chart:

A simple example is given below to demonstrate when the binomial distribution is suitable and how to find
the expected value and binomial probability:

Question: Afair die of six faces is thrown 10 times,
a) Find the expected value of getting a '3' in 10 throws.
b) Find the probabilities of getting a '3'four times.

Before answering the question, you should:

-":. ":. Gheck il the conditions for a binomial distribution are all satisfied.
i) n independent trials
ii) only 2 possible outcomes for each trial- success or failure
iii) The probability of success at each trial is constant

tA trial is throwing a die and the outcome of each trial does not affect that of the next trial
)Obtaining a '3'face up is a 'success', not obtaining a '3'is a 'failure'.
1
)The probability of getting a '3' at each trial is . tnis does not change from trial to trial.
6
*fo Ert."a tne following from the information given:

i) The value of ,r, the number of trials
ii) P = P1rrrr.""",

=
iii) P(failure) l- p
)n = 10 as the die is thrown 10 times.
1
rP(3) - 2
)P(3): I r- s
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