Question

Box-I contains 8 red (R₁₁, R₁₂, R₁₃) and 2 blue (B₁₁, B₁₂) marbles while Box-II contains 2 red(R₂₁, R₂₂) and 4 blue (B₂₁, B₂₂, B₂₃, B₂₄) marbles. A fair coin is tossed. If the coin turns up heads, a marble is chosen from Box-I; if it turns up tails, a marble is chosen from Box-II. Describe the sample space.

Answer 1

 A coin is tossed, if the result is head, a marble is chosen from Box I, for tail, a marble is chosen from Box II.
S = {(H, R₁₁), (H, R₁₂), (H, R₁₃),
(H, B₁₁), (H, B₁₂), (T, R₂₁),
(T, R₂₂), (T, B₂₁), (T, B₂₂),
(T, B₂₃), (T, B₂₄)}.
∴ n(S) = 11.

Answer 2

Box-I contains 3 red and 2 blue marbles
i.e., (R11, Rl2, R13, B11, B12)
Box-II contains 2 red and 4 blue marbles
i.e., (R21, R22, B21, B22, B23, B24)
It is given that a fair coin is tossed and if the head comes then marble is chosen from box-I otherwise it is chosen from box-II
∴ the sample space is
S = {(H, R₁₁), (H, R₁₂), (H, R₁₃), (H, B₁₁), (H, B₁₂), (T, R₂₁), (T, R₂₂), (T, B₂₁), (T, B₂₂), (T, B₂₃), (T, B₂₄)}.
∴ n(S) = 11

Answer 3

Box-I contains 3 red and 2 blue marbles
i.e., (R11, Rl2, R13, B11, B12)
Box-II contains 2 red and 4 blue marbles
i.e., (R21, R22, B21, B22, B23, B24)
It is given that a fair coin is tossed and if the head comes then marble is chosen from box-I otherwise it is chosen from box-II
∴ the sample space is
S = {(H, R₁₁), (H, R₁₂), (H, R₁₃), (H, B₁₁), (H, B₁₂), (T, R₂₁), (T, R₂₂), (T, B₂₁), (T, B₂₂), (T, B₂₃), (T, B₂₄)}.
∴ n(S) = 11