## Thursday, 23 February 2012

### Binomial Experiments

Hi friends,Previously we have discussed about multiplying polynomials worksheet and topic we are going to discuss today is binomial experiments which is a part of ap board of secondary education. The binomial experiments are part of the algebra mathematics. The binomial experiments are experiments in which have four conditions.
1 ) the number of trials are fix.
2 ) each trial is independent to others.
3 ) only two outcomes are possible.
4 ) the probability of each outcomes are constant from trial to trial.
These processes are performed with a fixed number of independent trials, each have two possible outcomes.
The binomial experiment examples: tossing a coin 10 times and see how many heads occur; Asking 100 people and find the result, if they watch xyz news; rolling a dice and see if the number 6 appears. Examples of the experiments that are not binomial experiments: rolling a dice a 6 appears (in this not a fixed number of trials), asking to the 10 people and how old they are (this means at least not two outcomes).
Binomial Probability example:
Two coins are tossed simultaneously 300 times and it is found that two heads appeared 135 times, one head appeared 111 times and no head appeared 54 times. If two coins are tossed at random, what is the probability of getting 1) 2 heads 2) 1 head 3) 0 head?
Solution : total number of trials = 135.
Number of times 1 head appears = 111.
Number of times 0 head appears = 54.
In a random toss of two coins, let e1, e2, e3 be the events of getting 2 heads, 1 head, 0 head respectively. Then, 1) p(getting 2 heads)=p(e1)= number of times 2 heads appear / total number of trials.
135 / 300 = 0.45
2) p (getting 1 head)= p(e2)= number of times 1 heads appear / total number of trials.
111 / 300=0.37
3)p(getting 0 head)= p(e 3 )= number of times no heads appear / total number of trials.
54 / 300=0.18
the possible outcomes are e1, e2, e3 and p(e1), p(e2), p(e3)=(0.45+0.37+0.18)=1
In the next session we are going to discuss Binomial Theorem and if anyone want to know about Properties of Complex Numbers then they can refer to Internet and text books for understanding it more precisely.
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