Question

A coin (H: heads; T: tails) is flipped and a number cube (1, 2, 3, 4, 5, 6) is rolled. What is the sample space for this experiment?

A. T1, T2, T3, T4, T5, T6
B. H, T, 1, 2, 3, 4, 5, 6
C. H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6
D. H1, H2, H3, H4, H5, H6

Answer 1

Answer: Choice C

Step-by-step explanation:

Start with the set {1, 2, 3, 4, 5, 6}

Stick "H" in front of each item to get {H1, H2, H3, H4, H5, H6} which represents half of the sample space. Something like H2 means "coin flipped heads and the number cube rolled a 2".

The other half of the sample space involves replacing each H with T. Which explains how we get T1, T2, T3, T4, T5, T6

Overall, the sample space is:

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

It might help to organize things into a table like this:

`\begin{array}c \cline{1-7}& 1 & 2 & 3 & 4 & 5 & 6\\\cline{1-7}H & H1 & H2 & H3 & H4 & H5 & H6\\\cline{1-7}T & T1 & T2 & T3 & T4 & T5 & T6\\\cline{1-7}\end{array}`

Or it could be written like this:

`\begin{array}c \cline{1-3}& H & T\\\cline{1-3}1 & H1 & T1\\\cline{1-3}2 & H2 & T2\\\cline{1-3}3 & H3 & T3\\\cline{1-3}4 & H4 & T4\\\cline{1-3}5 & H5 & T5\\\cline{1-3}6 & H6 & T6\\\cline{1-3}\end{array}`

Either table demonstrates how there are 6*2 = 12 items in the sample space.