Question
Rosa is attending an event where prizes are being given away. The probability of winning a T‑shirt is 0.89 and the probability of winning a $20 gift certificate is 0.05. Which statement correctly describes the chances of Rosa winning a T‑shirt or a $20 gift certificate?
A.
It is very likely that Rosa wins both prizes.
B.
It is very unlikely that Rosa wins either prize.
C.
It is very unlikely that Rosa wins a T‑shirt, but quite likely that she wins a gift certificate.
D.
It is very unlikely that Rosa wins a gift certificate, but quite likely that she wins a T‑shirt.
A.
It is very likely that Rosa wins both prizes.
B.
It is very unlikely that Rosa wins either prize.
C.
It is very unlikely that Rosa wins a T‑shirt, but quite likely that she wins a gift certificate.
D.
It is very unlikely that Rosa wins a gift certificate, but quite likely that she wins a T‑shirt.
Answers
Answered by
GPT-4o mini
To analyze Rosa's chances of winning a T-shirt or a $20 gift certificate, we need to look at the given probabilities:
- Probability of winning a T-shirt: \( P(T) = 0.89 \)
- Probability of winning a $20 gift certificate: \( P(G) = 0.05 \)
Now, let's consider the statements:
A. **It is very likely that Rosa wins both prizes.**
This statement is incorrect since the probability of winning a T-shirt is very high, but the probability of winning a gift certificate is quite low. Winning both at the same time is also contingent on the independence of these events, which we can't assume without specific information.
B. **It is very unlikely that Rosa wins either prize.**
This statement is incorrect. The probability of winning a T-shirt alone is 0.89, which indicates a very high chance of winning at least one prize.
C. **It is very unlikely that Rosa wins a T-shirt, but quite likely that she wins a gift certificate.**
This statement is incorrect. Rosa has a very high probability of winning a T-shirt (0.89), making it unlikely she won't win one.
D. **It is very unlikely that Rosa wins a gift certificate, but quite likely that she wins a T-shirt.**
This statement is correct. With a probability of winning a T-shirt at 0.89, it is quite likely she will win that prize. Conversely, with a probability of 0.05 for winning a gift certificate, it is indeed very unlikely that she will win that prize.
Therefore, the correct answer is:
**D. It is very unlikely that Rosa wins a gift certificate, but quite likely that she wins a T-shirt.**
- Probability of winning a T-shirt: \( P(T) = 0.89 \)
- Probability of winning a $20 gift certificate: \( P(G) = 0.05 \)
Now, let's consider the statements:
A. **It is very likely that Rosa wins both prizes.**
This statement is incorrect since the probability of winning a T-shirt is very high, but the probability of winning a gift certificate is quite low. Winning both at the same time is also contingent on the independence of these events, which we can't assume without specific information.
B. **It is very unlikely that Rosa wins either prize.**
This statement is incorrect. The probability of winning a T-shirt alone is 0.89, which indicates a very high chance of winning at least one prize.
C. **It is very unlikely that Rosa wins a T-shirt, but quite likely that she wins a gift certificate.**
This statement is incorrect. Rosa has a very high probability of winning a T-shirt (0.89), making it unlikely she won't win one.
D. **It is very unlikely that Rosa wins a gift certificate, but quite likely that she wins a T-shirt.**
This statement is correct. With a probability of winning a T-shirt at 0.89, it is quite likely she will win that prize. Conversely, with a probability of 0.05 for winning a gift certificate, it is indeed very unlikely that she will win that prize.
Therefore, the correct answer is:
**D. It is very unlikely that Rosa wins a gift certificate, but quite likely that she wins a T-shirt.**
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