Wednesday 28 October 2015

PROBABILITY 1




Given the interval of 1-15 inclusive, Find the probability of having an even number or a multiple of four.

Solution

This is a non-mutually exclusive event.
n(S) = number of sample space = 15.

Let P(E)= probability of even numbers = 7/15
Let P(M)= probability of multiple of four = 3/15
P(EnM) = probability of having both even and multiple of 4 = 3/15

P(EuM) = P(E) + P(M)  - P(EnM).

 P(EuM) =  7  +  33
                15    15   15

P(EuM) =  10  -   3 
                15     15  

P(EuM) =  7 
                15      

Hence probability of an even number or a multiple of four is 7/15.


TRY THIS……………

Given the interval of 1-15 inclusive, Find the probability of having an even number or a prime number.


REGULAR POLYGONS 2




Find the exterior angle of a regular polygon with 60 sides.

Solution

n = 60

i =   360
         60

i =   360
         60

i =   360
        60

i = 60

Hence the interior angle is 60

TRY THIS………………………………………..

Find the exterior angle of a regular polygon with 12 sides.

ALGEBRA 1




Expand 5x(4x – 5)

Solution

= 5x(4x – 5)

= (5x x 4x) – (5x x 5)

= 20x2 – 25x
 
Hence 5x(4x – 5) = 20x2 – 25x

TRY THIS……………

Expand 6a(7a – 4)

EXPONENTIALS 1





simplify 3
              8-2/3

Solution
=  3
    8-2/3

=  3 x 1
           8-2/3

=  3 x 82/3        [Since 1/a-n = an]

=  3 x (81/3)2        [Since 81/3 = cube root of 8 = 2]

=  3 x (2)2        

=  3 x 4

= 12        
         
Hence   3        = 12
              8-2/3

TRY THIS………………………………..

simplify   3
               125-2/3


LOGARITHMS 1




Evaluate Log26.4 - Log210 + Log2200

Solution

= Log26.4 - Log210 + Log2200

= Log2(6.4x200)
               10

= Log2(1280)
              10

= Log2(128)
            
= Log227)

= 7Log22

= 7 x 1

= 7

Hence Log26.4 - Log210 + Log2200 = 7 


TRY THIS…………………….

Evaluate Log21.6 - Log220 + Log2 3200