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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.



Answer :

GinnyAnswer
Let's go through the options one by one to determine which event corresponds to exactly one outcome of the experiment.

1. Event A: Both numbers are 5
- Rolling a die can give the numbers 1 through 6.
- Drawing a card can give the numbers 1 through 10.
- The only outcome where both numbers are 5 is (5, 5). There is exactly one such pair.
- Thus, Event A corresponds to exactly one outcome.

2. Event B: Neither number is a 5
- There are multiple pairs where both numbers are not 5.
- For example, (1, 1), (1, 2), (1, 3), ..., (6, 10) excluding pairs like (5, x) and (x, 5).
- There are 45 such pairs.
- Hence, Event B corresponds to more than one outcome.

3. Event C: The sum of the numbers is 3
- There are multiple pairs whose sum is 3.
- For example, (1, 2) and (2, 1).
- There are 2 such pairs.
- Thus, Event C corresponds to more than one outcome.

4. Event D: One of the numbers is a 3
- There are multiple pairs where at least one number is 3.
- For example, (3, 1), (3, 2), ..., (3, 10), (1, 3), (2, 3), ..., (6, 3).
- There are 15 such pairs.
- Therefore, Event D corresponds to more than one outcome.

Given this detailed analysis, the event that corresponds to exactly one outcome is:

Option A: Both numbers are 5s.

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