Question

a box has four cards numbered 1, 2, 3, and 4.
trey 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 1.
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 number chosen is 1:

Explanation:

Step1: Determine sample space for coin toss

The coin toss has 2 outcomes: \(H\) (heads) and \(T\) (tails).

Step2: Combine with card - pick outcomes

For each coin - toss outcome (\(H\) or \(T\)), there are 4 card - pick outcomes (\(1\), \(2\), \(3\), \(4\)).
Using the rule of counting for combined events (if event \(A\) has \(m\) outcomes and event \(B\) has \(n\) outcomes, the combined event \(A\) and \(B\) has \(m\times n\) outcomes), here \(m = 2\) (coin toss) and \(n=4\) (card pick).
The sample - space elements are formed by pairing each coin - toss result with each card number.
The sample space \(S=\{H1,H2,H3,H4,T1,T2,T3,T4\}\).

Step3: Find outcomes for the event "number chosen is 1"

We look for elements in the sample space where the second part of the pair (the card number) is \(1\).
The event \(E=\{H1,T1\}\)

Answer:

Sample space: \(H1,H2,H3,H4,T1,T2,T3,T4\)
Event that the number chosen is \(1\): \(H1,T1\)