Choose the best answer. If necessary, use the paper you were given.
A bowl contains 6 green grapes, 10 red grapes, and 8 black grapes.Which of the following is the correct calculation for the probability of choosing a red grape and then without putting the red grape back into the bowl, choosing a green grape?
- A. 10/24+6/24
- B. 10/24+6/23
- C. 10/24*6/24
- D. 10/24*6/23
Correct Answer & Rationale
Correct Answer: D
To determine the probability of selecting a red grape followed by a green grape without replacement, the first step involves calculating the probability of the first event (selecting a red grape). There are 10 red grapes out of a total of 24 grapes, giving a probability of 10/24. After choosing a red grape, there are now 23 grapes left in the bowl, including 6 green grapes. Thus, the probability of then selecting a green grape is 6/23. Option A incorrectly adds the probabilities, which is not appropriate for sequential events. Option B uses the correct second probability but fails to multiply the probabilities of the two events. Option C mistakenly adds both probabilities instead of multiplying them. Only option D correctly multiplies the probabilities of the two dependent events.
To determine the probability of selecting a red grape followed by a green grape without replacement, the first step involves calculating the probability of the first event (selecting a red grape). There are 10 red grapes out of a total of 24 grapes, giving a probability of 10/24. After choosing a red grape, there are now 23 grapes left in the bowl, including 6 green grapes. Thus, the probability of then selecting a green grape is 6/23. Option A incorrectly adds the probabilities, which is not appropriate for sequential events. Option B uses the correct second probability but fails to multiply the probabilities of the two events. Option C mistakenly adds both probabilities instead of multiplying them. Only option D correctly multiplies the probabilities of the two dependent events.
Other Related Questions
If the trend shown in the graph above continued into the next year, approximately how many sport utility vehicles were sold in 1999?
- A. 3 million
- B. 2.5 million
- C. 2 million
- D. 3 thousand
Correct Answer & Rationale
Correct Answer: A
To determine the approximate number of sport utility vehicles sold in 1999, analyzing the trend in the graph is essential. If the upward trend continued, sales would likely increase compared to previous years. Given the data, 3 million aligns with the projected growth rate, reflecting a significant rise consistent with market trends. Option B, 2.5 million, underestimates the growth, while C, 2 million, does not account for the upward trajectory. Option D, 3 thousand, is far too low and unrealistic, failing to represent the scale of SUV sales during that period. Thus, 3 million is the most reasonable estimate.
To determine the approximate number of sport utility vehicles sold in 1999, analyzing the trend in the graph is essential. If the upward trend continued, sales would likely increase compared to previous years. Given the data, 3 million aligns with the projected growth rate, reflecting a significant rise consistent with market trends. Option B, 2.5 million, underestimates the growth, while C, 2 million, does not account for the upward trajectory. Option D, 3 thousand, is far too low and unrealistic, failing to represent the scale of SUV sales during that period. Thus, 3 million is the most reasonable estimate.
What is the range of her scores?
- A. 100
- B. 120
- C. 440
- D. 2,250
Correct Answer & Rationale
Correct Answer: B
To determine the range of her scores, we subtract the lowest score from the highest score. If the highest score is 220 and the lowest is 100, the calculation is 220 - 100 = 120, which represents the range. Option A (100) misrepresents the range as it does not account for the difference between the highest and lowest scores. Option C (440) and Option D (2,250) are excessively high and do not reflect the actual spread of scores based on the provided data. Thus, 120 accurately represents the range of her scores.
To determine the range of her scores, we subtract the lowest score from the highest score. If the highest score is 220 and the lowest is 100, the calculation is 220 - 100 = 120, which represents the range. Option A (100) misrepresents the range as it does not account for the difference between the highest and lowest scores. Option C (440) and Option D (2,250) are excessively high and do not reflect the actual spread of scores based on the provided data. Thus, 120 accurately represents the range of her scores.
If an item regularly costs d dollars and is discounted 12 percent, which of the following represents the discounted price in dollars?
- A. 0.12d
- B. 0.88d
- C. 1.12d
- D. d-0.12
Correct Answer & Rationale
Correct Answer: B
To find the discounted price after a 12 percent discount on an item that costs d dollars, we first calculate the amount of the discount, which is 12% of d, or 0.12d. To determine the final price, we subtract this discount from the original price: d - 0.12d = 0.88d. Option A (0.12d) represents only the discount amount, not the final price. Option C (1.12d) incorrectly suggests an increase in price. Option D (d - 0.12) does not account for the percentage; it inaccurately represents the discount as a flat dollar amount rather than a percentage of the original price. Thus, 0.88d correctly reflects the discounted price.
To find the discounted price after a 12 percent discount on an item that costs d dollars, we first calculate the amount of the discount, which is 12% of d, or 0.12d. To determine the final price, we subtract this discount from the original price: d - 0.12d = 0.88d. Option A (0.12d) represents only the discount amount, not the final price. Option C (1.12d) incorrectly suggests an increase in price. Option D (d - 0.12) does not account for the percentage; it inaccurately represents the discount as a flat dollar amount rather than a percentage of the original price. Thus, 0.88d correctly reflects the discounted price.
If the values of x and y are negative, which of the following values must be positive?
- A. x²-y²
- B. x/y
- C. x+y
- D. x-y
Correct Answer & Rationale
Correct Answer: B
When both x and y are negative, the quotient \( x/y \) results in a positive value. This is because dividing a negative number by another negative number yields a positive outcome. Option A, \( x^2 - y^2 \), can be either positive or negative depending on the magnitudes of x and y; thus, it is not guaranteed to be positive. Option C, \( x + y \), is the sum of two negative numbers, which will always be negative. Option D, \( x - y \), involves subtracting a negative (y) from another negative (x), which can also yield a negative or zero result, depending on their values. Only \( x/y \) is assuredly positive.
When both x and y are negative, the quotient \( x/y \) results in a positive value. This is because dividing a negative number by another negative number yields a positive outcome. Option A, \( x^2 - y^2 \), can be either positive or negative depending on the magnitudes of x and y; thus, it is not guaranteed to be positive. Option C, \( x + y \), is the sum of two negative numbers, which will always be negative. Option D, \( x - y \), involves subtracting a negative (y) from another negative (x), which can also yield a negative or zero result, depending on their values. Only \( x/y \) is assuredly positive.