Question

a box has four cards numbered 1, 2, 3, and 4. dante will toss a coin once and record the toss as heads (h) or tails (t). then he 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 number chosen is 2. use the format h1 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 number chosen is 2 : {}

Explanation:

Step1: List all H + card pairs

$H1, H2, H3, H4$

Step2: List all T + card pairs

$T1, T2, T3, T4$

Step3: Combine for sample space

Combine all pairs from Step1 and Step2.

Step4: Extract number=2 outcomes

Select pairs with number 2.

Answer:

Sample space: $\{H1, H2, H3, H4, T1, T2, T3, T4\}$
Event that the number chosen is 2 : $\{H2, T2\}$