Paper 4: Fundamentals of Business Mathematics & Statistic

10.8 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Theoretical Distribution

Example 7 :

The probability that an evening college student will graduate is 0.4. Determine the probability that out of

5 students (a) none, (b) one, and (c) atleast one will graduate.

Solution :

n = 5 p = 0.4

4

10

⎛⎞⎜ ⎟⎟

⎜⎜⎝⎠⎟⎟; q = 0.6 106

⎛⎞⎜ ⎟⎟

⎜⎜⎝⎠⎟⎟

()^5546

10 10

rnr rnr

Pr CpqrrC

− ⎛⎞⎛⎞−

==⎜⎜⎜⎜⎜⎜⎟⎟⎟⎟⎟⎟⎟⎟

⎝⎠⎝⎠

(a) The probability of zero success =

05

0

5 46

C 10 10

⎛⎞⎛⎞⎜⎜⎟⎟⎟⎟

⎜⎜⎜⎜⎝⎠⎝⎠⎟⎟⎟⎟

=

6 5

1 ×⎛⎞⎜⎜⎝⎠⎜ 10 ⎟⎟⎟⎟

= 0.078

(b) The probability of one success =

5 4

1

46

C 10 10

××⎛⎞⎛⎞⎜⎜⎟⎟⎟⎟

⎜⎜⎜⎜⎝⎠⎝⎠⎟⎟⎟⎟

= 5 × 4 ×(6)^4

= 0.259

(c) The probability of atleast one success.

= 1– probability of no success

= 1– 0.078

= 0.922

Example 8 :

12 coins are tossed. What are the probabilities in a single tossing getting :

(1) 9 or more heads,

(2) less than 3 heads,

(3) atleast 8 heads

If the 12 coins are tossed 4096 times, or

(4) how many occasions would you expect these to be :

(a) less than 3 heads,

(b) atleast 2 heads,

(c) exactly 6 heads.

Solution :

(1) The probability of getting 9 or more heads is :

P(9) + P(10) + P(11) + P(12)

P(9) =

12 93

9

11

C 22

⎛⎞⎛⎞⎜⎜⎟⎟⎟⎟

⎜⎜⎜⎜⎝⎠⎝⎠⎟⎟⎟⎟