# 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. - Mathematics and Statistics

Sum

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.

#### Solution 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.

#### Solution 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

#### Solution 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

Concept: Introduction of Probability
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