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 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 1:

Explanation:

Step1: Find the sample space

The coin has 2 outcomes (\(H\) or \(T\)) and the card has 4 outcomes (\(1\), \(2\), \(3\), \(4\)).
By the counting principle, the total number of outcomes in the sample space is \(2\times4 = 8\).
The sample - space is formed by pairing each coin - toss outcome with each card - pick outcome.
The sample space \(S=\{H1,H2,H3,H4,T1,T2,T3,T4\}\)

Step2: Find the event that the number chosen is 1

We look for the outcomes in the sample space where the second part of the pair (the 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: \(H1,T1\)