SCAT - School and College Ability Data Interpretation and Probability Questions and Answers 1 — Questions and Answers
Question 1: The table below shows the number of different colored balls in a bag. If one ball is drawn at random, what is the probability that the ball is NOT blue? | Color | Number of Balls | |--------|-----------------| | Red | 8 | | Blue | 5 | | Green | 10 | | Yellow | 2 |
- 1/5
- 4/5 (Correct answer)
- 1/4
- 3/5
Correct answer: 4/5
First, calculate the total number of balls: 8 + 5 + 10 + 2 = 25. The number of balls that are not blue is the total number of balls minus the number of blue balls: 25 - 5 = 20. The probability of drawing a ball that is not blue is the number of non-blue balls divided by the total number of balls: 20/25, which simplifies to 4/5.
Question 2: A fair six-sided die is rolled and a fair coin is flipped. What is the probability of rolling an even number and the coin landing on tails?
- 1/6
- 1/2
- 1/4 (Correct answer)
- 1/3
Correct answer: 1/4
The probability of rolling an even number (2, 4, or 6) on a six-sided die is 3 out of 6, or 1/2. The probability of a fair coin landing on tails is 1/2. Since these are independent events, you multiply their probabilities to find the probability of both occurring: (1/2) * (1/2) = 1/4.
Question 3: The line graph shows the number of books a student read each month over a 5-month period: January (4), February (6), March (3), April (7), May (5). What is the average (mean) number of books read per month?
- 6
- 4
- 3
- 5 (Correct answer)
Correct answer: 5
To find the mean, sum the number of books read each month and divide by the number of months. Total books = 4 + 6 + 3 + 7 + 5 = 25. Number of months = 5. The mean is 25 / 5 = 5 books per month.
Question 4: A drawer contains 12 red socks and 14 blue socks. What is the minimum number of socks you must pull from the drawer in the dark to guarantee you have a matching pair?
- 3 (Correct answer)
- 2
- 13
- 26
Correct answer: 3
This is an application of the pigeonhole principle. In the worst-case scenario, you could pick one red sock and then one blue sock. The third sock you pick must be either red or blue, thus guaranteeing a match with one of the first two socks. Therefore, you must pull 3 socks.
Question 5: A pie chart represents a survey of 120 students' favorite sports. Soccer accounts for 30% of the circle. How many students chose soccer as their favorite sport?
- 30
- 40
- 36 (Correct answer)
- 24
Correct answer: 36
To find the number of students who chose soccer, you need to calculate 30% of the total number of students. Convert the percentage to a decimal (30% = 0.30) and multiply by the total number of students: 0.30 * 120 = 36 students.
Question 6: The bar chart below shows the scores of a class on a science test. Which of the following statements is true based on the data? - Score of 75: 5 students - Score of 80: 8 students - Score of 85: 6 students - Score of 90: 5 students - Score of 95: 2 students
- The mode of the scores is 90.
- More students scored 95 than 75.
- The total number of students who took the test is 25.
- The score of 80 was the most frequent score. (Correct answer)
Correct answer: The score of 80 was the most frequent score.
The mode is the value that appears most frequently in a data set. By looking at the number of students for each score, the score of 80 has the highest frequency (8 students). Therefore, the statement that the score of 80 was the most frequent is true.
SCAT - School and College Ability Data Interpretation and Probability Questions and Answers 1
The table below shows the number of different colored balls in a bag.
If one ball is drawn at random, what is the probability that the ball is NOT blue?
| Color | Number of Balls |
|--------|-----------------|
| Red | 8 |
| Blue | 5 |
| Green | 10 |
| Yellow | 2 |