Question

a box has four cards numbered 1, 2, 3, and 4. maya 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 tails. 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 coin toss is tails:

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 is \(2\times4 = 8\).
The sample - space is formed by combining 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 for tails

We need to pick the outcomes from the sample space where the coin - toss part is \(T\).
The event \(E=\{T1,T2,T3,T4\}\)

Answer:

Sample space: \(H1,H2,H3,H4,T1,T2,T3,T4\)
Event that the coin toss is tails: \(T1,T2,T3,T4\)