Out of quadrilaterals- Square , rectangle, rhomous, parallelogram and trapezium , a quadrilateral is chosen a radom . Find the probability that the quadrilateral chosen has
(i) All the angles right angles .
(ii) both the Diagonals are perpendicular to each other.
(iii) the diagonals bisect each other.

Answer

To solve the problem step by step, we will analyze the quadrilaterals given and calculate the probabilities for each condition.

### Step 1: Identify the Quadrilaterals
The quadrilaterals given are:
1. Square
2. Rectangle
3. Rhombus
4. Parallelogram
5. Trapezium

### Step 2: Define the Total Number of Quadrilaterals (N of S)
The total number of quadrilaterals (N of S) is 5, since we have 5 different types of quadrilaterals.

### Step 3: (i) Find the Probability that the Quadrilateral has All Angles as Right Angles
- The quadrilaterals that have all angles as right angles are:
- Square
- Rectangle

Thus, the number of favorable outcomes (N of A) is 2.

**Probability (P of A)** = N of A / N of S = 2 / 5

### Step 4: (ii) Find the Probability that the Quadrilateral has Both Diagonals Perpendicular to Each Other
- The quadrilaterals that have diagonals perpendicular to each other are:
- Square
- Rhombus

Thus, the number of favorable outcomes (N of B) is 2.

**Probability (P of B)** = N of B / N of S = 2 / 5

### Step 5: (iii) Find the Probability that the Quadrilateral has Diagonals that Bisect Each Other
- The quadrilaterals that have diagonals that bisect each other are:
- Square
- Rectangle
- Rhombus
- Parallelogram

Thus, the number of favorable outcomes (N of C) is 4.

**Probability (P of C)** = N of C / N of S = 4 / 5

### Summary of Probabilities
1. Probability that the quadrilateral has all angles as right angles: **2/5**
2. Probability that the quadrilateral has both diagonals perpendicular to each other: **2/5**
3. Probability that the quadrilateral has diagonals that bisect each other: **4/5**