1. Problem: Find the probability of selecting a figure which is a parallelogram from the given figures: square, rectangle, rhombus, kite, and trapezium. 2. Formula: Probability = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} 3. Important rule: A parallelogram is a quadrilateral with both pairs of opposite sides parallel. Square, rectangle, and rhombus are parallelograms. Kite and trapezium are not. 4. Count favorable outcomes: square, rectangle, rhombus = 3 5. Total outcomes: 5 (square, rectangle, rhombus, kite, trapezium) 6. Calculate probability: $$ \text{Probability} = \frac{3}{5} $$ 7. Final answer: The probability of selecting a parallelogram is $\frac{3}{5}$. --- 1. Problem: The probability of a student passing any examination is $\frac{2}{3}$. Find the probability that the student will not pass any of the three examinations. 2. Formula: Probability of failing an exam = $1 - \text{Probability of passing} = 1 - \frac{2}{3} = \frac{1}{3}$ 3. Since exams are independent, probability of failing all three exams is: $$ \left(\frac{1}{3}\right)^3 = \frac{1}{27} $$ 4. Final answer: The probability that the student will not pass any of the three exams is $\frac{1}{27}$.