Paper 4: Fundamentals of Business Mathematics & Statistic

FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 10.3

PASCAL’S TRIANGLE

(Showing coefficients of terms (p + q)n

Value of n Binomial coefficients Sum (2n)

1112

21214

3 1331 8

4 14641 16

51510105132

6 1 6 152015 6 1 64

7 1 7 21353521 7 1 128

8 1 8 2856705628 8 1 256

9 1 9 36 84 126 126 84 36 9 1 512

10 1 10 45 120 210 252 210 120 45 10 1 1,024

It can be easily seen that taking the first and last terms as 1, each term in the above can be obtained by
addingthe two-terms on either side of it in the preceding line i.e. the line above it. For instance, in line four,
6 is obtained by adding 3 and 3 in the third line; in line ten, 120 is obtained by adding 36 and 84 and in the
same line 120 is obtained by adding 84 and 36 and so on.
Probability for Number of Heads (Successes)
Number of successes (x) Probability (p)
0 nC 0 p^0 qn = qn
1 nC 1 pqn–1
2 nC 2 p^2 qn–2
3 nC 3 p^3 qn–3
r nCrprq(x–r)
n nCnpnq^0 = pn

Example 1 :
A coin is tossed six times. What is the probability of obtaining (a) 4 heads, (b) 5 heads, (c) 6 heads and
(d)getting 4 or more heads :
Solution :
(a) Probability of 4 heads

=

642 42

4

15 11 0.234

Cpq 22

=× =⎛⎞⎛⎞⎜⎜⎟⎟⎟⎟

⎜⎜⎜⎜⎝⎠⎝⎠⎟⎟⎟⎟

(b) Probability of 5 heads

=

5

(^6556011) .094
Cpq 22
=× =⎛⎞⎛⎞⎜⎜⎟⎟⎟⎟
⎜⎜⎜⎜⎝⎠⎝⎠⎟⎟⎟⎟