1. Binomial Distribution
Situations often arise where success or failure are the only options, such situations result in a binomial distribution.
To use the binomial distribution the following conditions must apply:
F the number of trials must be fixed
I each trial must be independent of the other
S the probability of success at each trial must
be the same
T there are only two outcomes, success or failure

2. We use the parameters n,π and x for the binomial distribution
n is the number of trials conducted
x is the total number of successes in n trials
π is the probability of success for each trial
1-π is the probability of failure
If all the conditions are met then the following binomial distribution formula can be used to find probabilities
We use the parameters X~B(n,π)
P(X=x)= 0≤x≤n xεW

3. eg. Traffic experts have determined that 1% of all drivers do not wear seatbelts.
If ten motorists are stopped at one particular intersection , what is the probability that
One motorist stopped is not wearing a seatbelt.
X~B(10,0.01) NB P(failure)=1-0.01
= 0.99
P(X=1)= =
= (0.01)(0.99)9
= (4sf)

4. X~B(10,0.01) ie the probability of 0 successes P(X=0) = =
(ii) All people stopped are wearing seatbelts
ie the probability of 0 successes
X~B(10,0.01)
P(X=0) = =
= 1×1×(0.99)10
= (4sf)

5. No more than one of the drivers who are stopped are not wearing a seatbelt
P(X≤1)
=P(X=1)+P(X=0) =
= (4sf)