A child’s game has 8 triangles (3 blue, 5 red) and 10 squares (6 blue, 4 red). One piece is lost at random. Find the probability it is (i) a triangle (ii) a square (iii) a blue square (iv) a red triangle.
(i) \(\dfrac{4}{9}\), (ii) \(\dfrac{5}{9}\), (iii) \(\dfrac{1}{3}\), (iv) \(\dfrac{5}{18}\)
Step 1: Write down the given information.
Total pieces = 8 + 10 = 18.
Step 2: Recall probability formula.
Probability of an event = \( \dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \).
(i) Probability of a triangle
Number of triangles = 8. Total pieces = 18.
So, \( P(\text{triangle}) = \dfrac{8}{18} = \dfrac{4}{9} \).
(ii) Probability of a square
Number of squares = 10. Total pieces = 18.
So, \( P(\text{square}) = \dfrac{10}{18} = \dfrac{5}{9} \).
(iii) Probability of a blue square
Number of blue squares = 6. Total pieces = 18.
So, \( P(\text{blue square}) = \dfrac{6}{18} = \dfrac{1}{3} \).
(iv) Probability of a red triangle
Number of red triangles = 5. Total pieces = 18.
So, \( P(\text{red triangle}) = \dfrac{5}{18} \).
Final Answer:
(i) \(\dfrac{4}{9}\), (ii) \(\dfrac{5}{9}\), (iii) \(\dfrac{1}{3}\), (iv) \(\dfrac{5}{18}\).