QUESTION 14
Easy
List the elements of a sample space for the simultaneous tossing of a coin and drawing of a card from a set of 6 cards numbered 1 through 6.
SOLUTION
When a coin is tossed, the possible outcomes are:
\(H(Head)\), \(T(Tail)\)
When a card is drawn from cards numbered \(1\) through \(6\), the possible outcomes are:
\(1, 2, 3, 4, 5, 6\)
For the simultaneous tossing of coin and drawing of a card, we combine each coin outcome with each card number.
Sample space, \(S = \{(H,1),(H,2),(H,3),(H,4),(H,5),(H,6),(T,1),(T,2),(T,3),(T,4),(T,5),(T,6)\}\)
\(H(Head)\), \(T(Tail)\)
When a card is drawn from cards numbered \(1\) through \(6\), the possible outcomes are:
\(1, 2, 3, 4, 5, 6\)
For the simultaneous tossing of coin and drawing of a card, we combine each coin outcome with each card number.
Sample space, \(S = \{(H,1),(H,2),(H,3),(H,4),(H,5),(H,6),(T,1),(T,2),(T,3),(T,4),(T,5),(T,6)\}\)
🏆
Final Answer : S = {(H,1),(H,2),(H,3),(H,4),(H,5),(H,6),(T,1),(T,2),(T,3),(T,4),(T,5),(T,6)}.
Concept Note
For combined experiments:
(i) Write the outcomes of each experiment separately.
(ii) Pair every outcome of the first experiment with every outcome of the second experiment.