Mallory loaded 200 digital pictures into a digital picture frame. 78 are pictures of family members, 26 are pictures of pets, the rest are pictures of friends. The frame displays one picture every 10 seconds. Which value is closest to the probability that the next picture the frame displays will be a picture of a friend?
- A. 0.33
- B. 0.43
- C. 0.48
- D. 0.52
- E. 0.96
Correct Answer & Rationale
Correct Answer: C
To find the probability that the next picture displayed is of a friend, first calculate the total number of friend pictures. There are 200 total pictures, with 78 family and 26 pet pictures, leaving 200 - 78 - 26 = 96 pictures of friends. The probability is then the number of friend pictures divided by the total: 96/200 = 0.48. Option A (0.33) underestimates the proportion of friend pictures. Option B (0.43) is also lower than the calculated probability. Option D (0.52) slightly overestimates it, and option E (0.96) is far too high, misrepresenting the actual count. Thus, 0.48 accurately reflects the likelihood of displaying a friend picture next.
To find the probability that the next picture displayed is of a friend, first calculate the total number of friend pictures. There are 200 total pictures, with 78 family and 26 pet pictures, leaving 200 - 78 - 26 = 96 pictures of friends. The probability is then the number of friend pictures divided by the total: 96/200 = 0.48. Option A (0.33) underestimates the proportion of friend pictures. Option B (0.43) is also lower than the calculated probability. Option D (0.52) slightly overestimates it, and option E (0.96) is far too high, misrepresenting the actual count. Thus, 0.48 accurately reflects the likelihood of displaying a friend picture next.
Other Related Questions
The expression 6a + 4c represents the total price, in dollars, of admission to an air show for a adults and c children. On Saturday, 380 adults and 120 children paid admission to the air show. What was the total price of admission for those people?
- A. 524
- B. 2240
- C. 2760
- D. 5000
- E. 12000
Correct Answer & Rationale
Correct Answer: C
To find the total price of admission, substitute the values of adults (a) and children (c) into the expression 6a + 4c. Here, a = 380 and c = 120. Calculating: 6(380) + 4(120) = 2280 + 480 = 2760. Thus, the total price is 2760 dollars. Option A (524) is too low, as it doesn't account for the number of attendees. Option B (2240) underestimates the total, likely misunderstanding the pricing structure. Option D (5000) and Option E (12000) are excessively high, suggesting a miscalculation or misunderstanding of the pricing per adult and child.
To find the total price of admission, substitute the values of adults (a) and children (c) into the expression 6a + 4c. Here, a = 380 and c = 120. Calculating: 6(380) + 4(120) = 2280 + 480 = 2760. Thus, the total price is 2760 dollars. Option A (524) is too low, as it doesn't account for the number of attendees. Option B (2240) underestimates the total, likely misunderstanding the pricing structure. Option D (5000) and Option E (12000) are excessively high, suggesting a miscalculation or misunderstanding of the pricing per adult and child.
In tennis, a player has two chances to serve the ball successfully. Tamara is successful 70% of the time on her first serve. Tamara is successful 80% of the time on her second serve. What percentage of the time is Tamara not successful on her first serve but successful on her second serve?
- A. 5%
- B. 14%
- C. 24%
- D. 50%
- E. 56%
Correct Answer & Rationale
Correct Answer: B
To determine the percentage of time Tamara is not successful on her first serve but successful on her second serve, first calculate the probability of her missing the first serve, which is 30% (100% - 70%). Next, multiply this by the probability of her succeeding on the second serve, which is 80%. Thus, the calculation is 0.30 (failure on first serve) x 0.80 (success on second serve) = 0.24, or 24%. Option A (5%) underestimates the failure rate. Option C (24%) is the correct calculation but misrepresents the context. Option D (50%) assumes equal success rates, which is inaccurate. Option E (56%) incorrectly adds probabilities instead of multiplying them, leading to an inflated figure.
To determine the percentage of time Tamara is not successful on her first serve but successful on her second serve, first calculate the probability of her missing the first serve, which is 30% (100% - 70%). Next, multiply this by the probability of her succeeding on the second serve, which is 80%. Thus, the calculation is 0.30 (failure on first serve) x 0.80 (success on second serve) = 0.24, or 24%. Option A (5%) underestimates the failure rate. Option C (24%) is the correct calculation but misrepresents the context. Option D (50%) assumes equal success rates, which is inaccurate. Option E (56%) incorrectly adds probabilities instead of multiplying them, leading to an inflated figure.
What are the solutions to the equation: x² - 10?
- A. ±5
- B. ±√10
- C. ±10
- D. ±10²
- E. ±20
Correct Answer & Rationale
Correct Answer: B
To solve the equation \( x^2 - 10 = 0 \), we first isolate \( x^2 \) by adding 10 to both sides, resulting in \( x^2 = 10 \). Taking the square root of both sides gives us \( x = \pm\sqrt{10} \), which corresponds to option B. Option A, \( \pm5 \), is incorrect as \( 5^2 = 25 \), not 10. Option C, \( \pm10 \), is also wrong because \( 10^2 = 100 \). Option D, \( \pm10^2 \), misinterprets the operation, yielding \( \pm100 \), which is not relevant here. Lastly, option E, \( \pm20 \), is incorrect since \( 20^2 = 400 \). Thus, only option B accurately represents the solutions to the equation.
To solve the equation \( x^2 - 10 = 0 \), we first isolate \( x^2 \) by adding 10 to both sides, resulting in \( x^2 = 10 \). Taking the square root of both sides gives us \( x = \pm\sqrt{10} \), which corresponds to option B. Option A, \( \pm5 \), is incorrect as \( 5^2 = 25 \), not 10. Option C, \( \pm10 \), is also wrong because \( 10^2 = 100 \). Option D, \( \pm10^2 \), misinterprets the operation, yielding \( \pm100 \), which is not relevant here. Lastly, option E, \( \pm20 \), is incorrect since \( 20^2 = 400 \). Thus, only option B accurately represents the solutions to the equation.
A bowl contains 18 pieces of candy: 8 red, 6 orange, and 4 green. Brandon will select 1 piece of candy at random. What is the probability that Brandon will select a green piece?
- A. 2/7
- B. 2/9
- C. 2/11
- D. 1/9
- E. 1/8
Correct Answer & Rationale
Correct Answer: B
To find the probability of selecting a green piece of candy, divide the number of green candies by the total number of candies. There are 4 green candies and 18 total candies, resulting in a probability of 4/18, which simplifies to 2/9. Option A (2/7) incorrectly assumes a different total or count of green candies. Option C (2/11) suggests an inaccurate total of candies or green pieces. Option D (1/9) miscalculates the ratio of green candies to the total. Option E (1/8) also misrepresents the count of green candies. Only B accurately reflects the correct ratio.
To find the probability of selecting a green piece of candy, divide the number of green candies by the total number of candies. There are 4 green candies and 18 total candies, resulting in a probability of 4/18, which simplifies to 2/9. Option A (2/7) incorrectly assumes a different total or count of green candies. Option C (2/11) suggests an inaccurate total of candies or green pieces. Option D (1/9) miscalculates the ratio of green candies to the total. Option E (1/8) also misrepresents the count of green candies. Only B accurately reflects the correct ratio.