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  +  3 – 3

                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 8^2/3        [Since 1/a^-n = aⁿ]

=  3 x (8^1/3)²        [Since 8^1/3 = 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