Paper 4: Fundamentals of Business Mathematics & Statistic

FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 10.9

P(10) =

12 10 2

10

11

C 22

⎛⎞⎛⎞⎜⎜⎟⎟⎟⎟

⎜⎜⎜⎜⎝⎠⎝⎠⎟⎟⎟⎟

P(11) =

12 11

11

11

C 22

⎛⎞⎛⎞⎜⎜⎟⎟⎟⎟

⎜⎜⎜⎜⎝⎠⎝⎠⎟⎟⎟⎟

P(12) =

12

12 12 1

C 2

⎛⎞⎜ ⎟⎟

⎜⎜⎝⎠⎟⎟

P(≥9) =

12 9312 10212 11 12 12

91 0 1 112

11 1 1 11 1

CC CC 22 2 2 22 2

⎛⎞⎛⎞ ⎛⎞⎛⎞ ⎛⎞⎛⎞ ⎛⎞⎜⎜ ⎜⎜ ⎜⎜ ⎜⎟⎟ ⎟⎟ ⎟⎟ ⎟⎟⎟ ⎟⎟ ⎟⎟ ⎟+++

⎜⎜ ⎜⎜ ⎜⎜ ⎜⎜⎜ ⎜⎜ ⎜⎜ ⎜⎝⎠⎝⎠ ⎝⎠⎝⎠ ⎝⎠⎝⎠ ⎝⎠⎟⎟ ⎟⎟ ⎟⎟ ⎟⎟⎟ ⎟⎟ ⎟⎟ ⎟

= ()

(^1212121212)
9101112

1

2 CC C C

⎧⎫⎪⎪⎪⎪⎪⎪⎛⎞⎜ ⎟

⎨⎬⎪⎪⎜⎜⎝⎠⎟⎟⎟ +++

⎪⎪⎪⎪⎩⎭

= 40961 ()220 66 12 1+++

= 4096299 or7.3%

(2) The probability of getting less than 3 heads:
P(>3) = P(0) + P(1) + P(2)

=

12 12 12

12 01211112 12

CCC 222

⎛⎞ ⎛⎞ ⎛⎞⎜⎜⎜⎟⎟⎟++

⎜⎜⎜⎜⎜⎜⎝⎠ ⎝⎠ ⎝⎠⎟⎟⎟⎟⎟⎟⎟⎟⎟

= ()

12

(^1120121212)
2 CCC

⎧⎫⎪⎪⎪⎪⎪⎪⎛⎞⎟

⎨⎬⎜⎜⎜ ⎟⎟⎟ ++

⎪⎪⎪⎪⎪⎪⎩⎭⎝⎠

= 40961 ()112 66++

= 409679

(3) Probability of atleast 8 heads :

Probability of 8 heads =

12 12

8

(^1495) 0.1208
C 2 4096

⎛⎞⎜ ⎟⎟ ==

⎜⎜⎝⎠⎟⎟

Probability of 8 heads == 4096299 0.073
Probability of atleast 8 heads = 0.1208 + 0.073 = 0.1938
(4) (a) Probability of less than 3 heads out of 4096 times

4096 79

× 4096 =79 Times