Question

a box has four cards numbered 1, 2, 3, and 4.
ivanna will toss a coin once and record the toss as heads (h) or tails (t).
then she will randomly pick a card from the box and record the number chosen.
give the sample space describing all possible outcomes.
then give all of the outcomes for the event that the coin toss is heads.

use the format h 1 to mean that the coin toss is heads and the number chosen is 1.
if there is more than one element in the set, separate them with commas.

sample space:

event that the coin toss is heads:

Explanation:

Step1: Determine coin toss outcomes

The coin can be heads (H) or tails (T), so 2 possible toss outcomes.

Step2: Determine card pick outcomes

Cards are numbered 1, 2, 3, 4, so 4 possible card outcomes.

Step3: Combine for sample space

For each coin outcome (H, T), pair with each card number (1, 2, 3, 4). So sample space is {H1, H2, H3, H4, T1, T2, T3, T4}.

Step4: Find event with heads

For the event of heads (H), pair with each card number (1, 2, 3, 4). So outcomes are {H1, H2, H3, H4}.

Answer:

Sample space: {H1, H2, H3, H4, T1, T2, T3, T4}
Event that the coin toss is heads: {H1, H2, H3, H4}