Asked by 2
Which answer correctly describes the probability of rolling a die that lands on a number less than
and drawing a card that is red or black?
Responses
even
even
certain
certain
likely
likely
impossible
impossible
unlikely
unlikely
and drawing a card that is red or black?
Responses
even
even
certain
certain
likely
likely
impossible
impossible
unlikely
unlikely
Answers
Answered by
GPT-4o mini
To find the correct answer, we need to analyze the two parts of the scenario: rolling a die and drawing a card.
1. **Rolling a die**: A standard die has six faces numbered 1 through 6. The numbers less than 3 on a die are 1 and 2. Therefore, the probability of rolling a die and landing on a number less than 3 is 2 out of 6, which simplifies to 1/3.
2. **Drawing a card**: In a standard deck of playing cards, there are 52 cards in total, consisting of 26 red cards (hearts and diamonds) and 26 black cards (clubs and spades). Thus, when you draw a card, the event of drawing a card that is either red or black is certain because all cards in the deck are either red or black.
Now let's analyze the combination of these two events:
- The first event (rolling less than 3) has a probability of 1/3.
- The second event (drawing a card that is red or black) has a probability of 1 (certain).
Since one part of the scenario (drawing a card) is certain, we look at how we can describe the overall probability of the combined scenario.
In simple terms, rolling a number less than 3 is "unlikely" (since it's only a 1 in 3 chance), but the event of drawing a card is "certain" (since you will always draw either a red or black card regardless of the die roll).
The overall probability characteristics for the two actions don't align perfectly, but since the event of drawing a card will always happen, it doesn't change the outcome to make the rolling event "more likely."
In this case, the best response among the provided options would be **unlikely** for the rolling part combined with the certainty of the drawing part.
Thus, the correct answer is: **unlikely (for the overall probability aspect when considered together)**.
1. **Rolling a die**: A standard die has six faces numbered 1 through 6. The numbers less than 3 on a die are 1 and 2. Therefore, the probability of rolling a die and landing on a number less than 3 is 2 out of 6, which simplifies to 1/3.
2. **Drawing a card**: In a standard deck of playing cards, there are 52 cards in total, consisting of 26 red cards (hearts and diamonds) and 26 black cards (clubs and spades). Thus, when you draw a card, the event of drawing a card that is either red or black is certain because all cards in the deck are either red or black.
Now let's analyze the combination of these two events:
- The first event (rolling less than 3) has a probability of 1/3.
- The second event (drawing a card that is red or black) has a probability of 1 (certain).
Since one part of the scenario (drawing a card) is certain, we look at how we can describe the overall probability of the combined scenario.
In simple terms, rolling a number less than 3 is "unlikely" (since it's only a 1 in 3 chance), but the event of drawing a card is "certain" (since you will always draw either a red or black card regardless of the die roll).
The overall probability characteristics for the two actions don't align perfectly, but since the event of drawing a card will always happen, it doesn't change the outcome to make the rolling event "more likely."
In this case, the best response among the provided options would be **unlikely** for the rolling part combined with the certainty of the drawing part.
Thus, the correct answer is: **unlikely (for the overall probability aspect when considered together)**.