Question

Describe the sample space for the following events:

1. A coin is tossed and a die is thrown.

2. A coin is tossed and then a die is rolled.

3. 2 boys and 2 girls are in a Room X and 1 boy and 3 girls in Room Y. Specify the sample space for the experiment in which a room is selected and then a person.

4. One die of red colour, one of white colour and one of blue colour are placed in a bag. One die is selected at random and rolled, its colour and the number on its upper most face is noted.

5. An experiment consists of tossing a coin and then throwing it second time if a head occur. If a tail occurs on the first toss, then a die is rolled once.

6. A coin is tossed. If the outcome is a head, a die is thrown. If the die shows up shows up an head, a die is thrown. If the die shows up an even number, the die is thrown again.

Answer 1

1. A coin is tossed then S₁ = {H, T}

A die is rolled then S₂ = {1, 2, 3, 4, 5, 6}

Hence sample space

S = {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}.

2. A coin is tossed then S₁ = {H, T}

A die is rolled then S₂ = {1, 2, 3, 4, 5, 6}

Hence sample space S = {H1, H2, H3,H4, H5,H6, T}

3. Let B₁, B₂ denote the boys and G₁, G₂ girls in room X, B₁ denote the boys and G₃, G₄, G₅ girls in room Y. Hence sample space

S = {XB₁, XB₂, XG₁, XG₂, YB₁, YG₃, XG₄, XG₅}

4. Three die are R,W, and B, then S₁ = {R, W, B)

A die is rolled then S₂ = {1, 2, 3, 4, 5, 6}

Hence sample space S = {R1, R2, R3, R4, R5, R6, W1, W2, W3, W4, W5, W6, B1, B2, B3, B4, B5, B6}

5. A coin is tossed then S₁ = {H, T}

A coin tossed again then S₂ = {H, T}

A die is rolled then S₃ = {1, 2, 3, 4, 5, 6}

Hence sample space

S = {HH, HT, T1, T2, T3, T4, T5, T6}

6. A coin is tossed then S₁ = {H, T}

When the coin shows T, then there is no action. When the coin shows H, a die is thrown

S₂ = {1, 2, 3, 4, 5, 6}

When the die shows {1, 3, 5}, then there is no action.

When the die shows {2, 4, 6}, then a die is thrown again.

Hence;

S = {T, H1, H3, H5, H21, H22, H23, H24, H25, H26, H41, H42, H43, H44, H45, H46,H61, H62, H63, H64, H65, H66}.