In a game for children, there are 8 triangles in which 3 are blue and

1.	In a game for children, there are 8 triangles in which 3 are blue and remaining red. Also, in this game there are 10 squares, in which 6 are blue and remaining red. One of these figure ¡s at random lost. Find the probabilities of following:(i) The lost figure is a triangle.(ii) It is a square.(iii) It is a blue square.(iv) It is a red triangle.
Answer» In the given game total number of figures = 8 (triangles) + 10 (squares) = 18 ∴ Number of all possible outcomes = 18 (i) Let the event of occurring a triangle be (T). ∴ The number of favourable outcomes of T = 8. ⇒ P(T) = \(\frac { 8 }{ 18 }\) = \(\frac { 4 }{ 9 }\) (ii) Let the event occurring a square be (S). ∴ The number of favourable outcomes of S = 10 ⇒ P(S) = \(\frac { 10 }{ 18 }\) = \(\frac { 5 }{ 9 }\) (iii) Let the event of occurring the blue squares be (B). ∴ There are 6 blue squares. ∴ The number of favourable outcomes of (B) = 6 ⇒ P(A) = \(\frac { 6 }{ 18 }\) = \(\frac { 1 }{ 3 }\) (iv) Let the event occurring red triangles be (P) The number of red triangles = 8 – 3 = 5 ∴ The number of favourable outcomes of (R) = 5 ⇒ P(R) = \(\frac { 5 }{ 18 }\)

In a game for children, there are 8 triangles in which 3 are blue and remaining red. Also, in this game there are 10 squares, in which 6 are blue and remaining red. One of these figure ¡s at random lost. Find the probabilities of following:(i) The lost figure is a triangle.(ii) It is a square.(iii) It is a blue square.(iv) It is a red triangle.

Answer»

In the given game total number of figures = 8 (triangles) + 10 (squares) = 18

∴ Number of all possible outcomes = 18

(i) Let the event of occurring a triangle be (T).

∴ The number of favourable outcomes of T = 8.

⇒ P(T) = \(\frac { 8 }{ 18 }\) = \(\frac { 4 }{ 9 }\)

(ii) Let the event occurring a square be (S).

∴ The number of favourable outcomes of S = 10

⇒ P(S) = \(\frac { 10 }{ 18 }\) = \(\frac { 5 }{ 9 }\)

(iii) Let the event of occurring the blue squares be (B).

∴ There are 6 blue squares.

∴ The number of favourable outcomes of (B) = 6

⇒ P(A) = \(\frac { 6 }{ 18 }\) = \(\frac { 1 }{ 3 }\)

(iv) Let the event occurring red triangles be (P)

The number of red triangles = 8 – 3 = 5

∴ The number of favourable outcomes of (R) = 5

⇒ P(R) = \(\frac { 5 }{ 18 }\)