EDUCATION FOR BETTER TOMMROW
Thursday, 7 August 2014
chapter-10 - Worked Out Examples – 3
A fair coin is tossed
times. Find the probability of obtaining
Consider any arbitrary sequence of
tosses that contains exactly
Heads. For example, consider
Any such sequence has a probability of occurrence equal to
Thus, what we need to do is count the number of sequences with exactly
Heads. The required probability will then be
(No. of sequences).
Counting such sequences is a simple
problem, and those familiar with that subject will immediately hit upon the answer: there are
In general, we see that
For this question, we consider all the possible cases and add their respective probabilities like this:
Similarly, we have
This questions was an example of Binomial Distributions, something we’ll study in more detail later in this chapter.
Consider the sequence of numbers
. A person chooses three numbers at random from this sequence. Find the probability that the three numbers form an
s can be formed with varying common differences
are examples of
. The maximum
, in the
Let us count all such
s in a table. Verify the column on the right.
Thus, the total number of
s possible from this set is
. Also, from this set of
numbers, a selection of
numbers can be made in
Therefore, the probability that three numbers picked at random from this set form an
August 07, 2014
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