Question

select the correct answer.
an experiment consists of rolling a six - sided die to select a number between 1 and 6 and drawing a card at random from a set of 10 cards numbered 1, 2, 3, ... 10. which event definition corresponds to exactly one outcome of the experiment?
a. both numbers are 5s.
b. neither number is a 5.
c. the sum of the numbers is 3.
d. one of the numbers is a 3.

Explanation:

Step1: Analyze Option A

An outcome here is (die roll=5, card draw=5). This is exactly one unique pair of results from the experiment.

Step2: Analyze Option B

This includes all outcomes where die ≠5 and card ≠5. There are $5 \times 9 = 45$ such outcomes, so it has multiple results.

Step3: Analyze Option C

The sum equals 3 with two possible pairs: (die=1, card=2) and (die=2, card=1). This has 2 outcomes.

Step4: Analyze Option D

This includes all outcomes where die=3 (any card, 10 outcomes) or card=3 (any die, 6 outcomes), minus the overlap (die=3, card=3) to avoid double-counting: $10 + 6 -1 =15$ outcomes.

Answer:

A. Both numbers are 5s.