Find the area of the irregular figure

The area of the irregular figure is

Step-by-step explanation:

we know that

The area of the irregular figure is equal to the area of rectangle plus the area of triangle

The area of rectangle is equal to

The area of triangle is equal to

Sum the areas

a) 0.3333

b) 0.2381

c) 0.0952

d) 0.4286

e) 0.4523

f) 0.2637

Step-by-step explanation:

The concept applied here is dependent probability or probability without REPLACEMENT

a) What is the probability that the first resistor is 100Ω?

P(first resistor 100Ω) = number of 100Ω / Total number of resistors

= 5/15 = 0.3333

b) P( second resistor 100 Ω, the first resistor 50 Ω?

= Since second resistor of 50Ω was drawn first, the total number of resistors would have reduced, but the 100Ω resistor still maintains its number

= 10/15 x 5/14 = 0.2381

c) P( second resistor is 100 Ω, the first resistor is 100 Ω)

In this case, since first resistor is drawn, the number of 100 Ω would have reduced so also the total number of resistors

= 5/15 x 4/14 = 0.0952

d) P( that the first two resistors are both 50Ω) = Implies picking 2- 50Ω

= 10/15 x 9/14 = 0.4286

e) P(total of two resistors are selected from the box) = P( first 100Ω and second- 50Ω) or P( First 50Ω and second 100Ω) = 10/15 x 5/14 + 5/15 x 9/14 = 0.4523

f) P( more than three resistors are selected from the box) = 1 - P( Less than or equals to three resistors) - it implies that the consideration is for the 100Ω

= P( 1resistor) - P( 2- Resistor) - P( 3- Resistor)

1 - 5/15 - (10/15 + 5/14) - (10/15 + 9/14 + 5/13)

= 0.2637