A bag contains two black, three green and four red balls. A ball is picked from the bag at random. What is the probability that it is either black or red?

Question

Asked on July 1, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

Accepted Answer · 2026-07-01T10:11:36.173Z

Here are the solutions to the questions: Question 29: A bag contains two black, three green, and four red balls. A ball is picked from the bag at random. What is the probability that it is either black or red? Step 1: Determine the total number of balls. Number of black balls = 2 Number of green balls = 3 Number of red balls = 4 Total number of balls = 2 + 3 + 4 = 9 Step 2: Determine the number of favorable outcomes (black or red balls). Number of black or red balls = Number of black balls + Number of red balls = 2 + 4 = 6 Step 3: Calculate the probability. The probability of picking a black or red ball is the ratio of favorable outcomes to the total number of outcomes. P(Black or Red) = Number of black or red ballsTotal number of balls = (6)/(9) Step 4: Simplify the probability. P(Black or Red) = (2)/(3) This corresponds to option A. The final answer is A. (2)/(3). Question 30: Two fair dice are thrown together once. Find the probability of getting two odd numbers. Step 1: Determine the total number of possible outcomes when two dice are thrown. Each die has 6 faces, so the total number of outcomes is 6 × 6 = 36. Step 2: Determine the number of odd outcomes for a single die. The odd numbers on a die are 1, 3, 5. There are 3 odd outcomes. Step 3: Determine the number of outcomes where both dice show an odd number. For the first die, there are 3 odd outcomes. For the second die, there are 3 odd outcomes. The number of outcomes where both are odd is 3 × 3 = 9. These outcomes are (1,1), (1,3), (1,5), (3,1), (3,3), (3,5), (5,1), (5,3), (5,5). Step 4: Calculate the probability of getting two odd numbers. P(two odd numbers) = Number of favorable outcomesTotal number of outcomes = (9)/(36) Step 5: Simplify the probability. P(two odd numbers) = (1)/(4) This corresponds to option A. The final answer is A. (1)/(4). Question 31: Solve for x in the equation (1)/(x) + (2)/(3x) = (1)/(6). Step 1: Find a common denominator for the terms on the left side of the equation. The least common multiple of x and 3x is 3x. (3)/(3x) + (2)/(3x) = (1)/(6) Step 2: Combine the fractions on the left side. (3+2)/(3x) = (1)/(6) (5)/(3x) = (1)/(6) Step 3: Cross-multiply to solve for x. 5 × 6 = 1 × 3x 30 = 3x Step 4: Divide by 3. x = (30)/(3) x = 10 This corresponds to option B. The final answer is B. 10. Question 32: Find the equation whose roots are 2(1)/(2) and (1)/(2). Step 1: Convert the mixed number root to an improper fraction. The roots are = 2(1)/(2) = (5)/(2) and = (1)/(2). Step 2: Calculate the sum of the roots. + = (5)/(2) + (1)/(2) = (6)/(2) = 3 Step 3: Calculate the product of the roots. = (5)/(2) × (1)/(2) = (5)/(4) Step 4: Form the quadratic equation using the formula x^2 - ( + )x + = 0. x^2 - (3)x + (5)/(4) = 0 x^2 - 3x + (5)/(4) = 0 Step 5: Multiply the entire equation by 4 to eliminate the fraction. 4(x^2 - 3x + (5)/(4)) = 4(0) 4x^2 - 12x + 5 = 0 This result does not directly match any of the given options. Self-correction/Assumption: It is common for such multiple-choice questions to have a typo in the provided values if the calculated answer doesn't match any option. If we assume the second root was intended to be 1(1)/(2) (or (3)/(2)) instead of (1)/(2), let's re-evaluate. If = (5)/(2) and = (3)/(2): Sum of roots: + = (5)/(2) + (3)/(2) = (8)/(2) = 4. Product of roots: = (5)/(2) × (3)/(2) = (15)/(4). The equation would be x^2 - 4x + (15)/(4) = 0. Multiplying by 4 gives 4x^2 - 16x + 15 = 0. This matches option C. Given the options, it is highly probable that the second root was intended to be 1(1)/(2). We will proceed with this assumption to select an option. The final answer is C. 4x^2 - 16x + 15 = 0. Question 33: If m = (4b^2)/(xy) + t, express t in terms of m, b, x and y. Step 1: Isolate the term containing t by subtracting (4b^2)/(xy) from both sides of the equation. m - (4b^2)/(xy) = t Step 2: Rewrite the equation with t on the left side. t = m - (4b^2)/(xy) Step 3: Combine the terms on the right side into a single fraction by finding a common denominator, which is xy. t = (m · xy)/(xy) - (4b^2)/(xy) t = (mxy - 4b^2)/(xy) This corresponds to option B. The final answer is B. t = (mxy - 4b^2)/(xy). That's 2 down. 3 left today — send the next one.

Accepted Answer · 2026-07-01T10:11:36.173Z

Here are the solutions to the questions: Question 29: A bag contains two black, three green, and four red balls. A ball is picked from the bag at random. What is the probability that it is either black or red? Step 1: Determine the total number of balls. Number of black balls = 2 Number of green balls = 3 Number of red balls = 4 Total number of balls = 2 + 3 + 4 = 9 Step 2: Determine the number of favorable outcomes (black or red balls). Number of black or red balls = Number of black balls + Number of red balls = 2 + 4 = 6 Step 3: Calculate the probability. The probability of picking a black or red ball is the ratio of favorable outcomes to the total number of outcomes. P(Black or Red) = Number of black or red ballsTotal number of balls = (6)/(9) Step 4: Simplify the probability. P(Black or Red) = (2)/(3) This corresponds to option A. The final answer is A. (2)/(3). Question 30: Two fair dice are thrown together once. Find the probability of getting two odd numbers. Step 1: Determine the total number of possible outcomes when two dice are thrown. Each die has 6 faces, so the total number of outcomes is 6 × 6 = 36. Step 2: Determine the number of odd outcomes for a single die. The odd numbers on a die are 1, 3, 5. There are 3 odd outcomes. Step 3: Determine the number of outcomes where both dice show an odd number. For the first die, there are 3 odd outcomes. For the second die, there are 3 odd outcomes. The number of outcomes where both are odd is 3 × 3 = 9. These outcomes are (1,1), (1,3), (1,5), (3,1), (3,3), (3,5), (5,1), (5,3), (5,5). Step 4: Calculate the probability of getting two odd numbers. P(two odd numbers) = Number of favorable outcomesTotal number of outcomes = (9)/(36) Step 5: Simplify the probability. P(two odd numbers) = (1)/(4) This corresponds to option A. The final answer is A. (1)/(4). Question 31: Solve for x in the equation (1)/(x) + (2)/(3x) = (1)/(6). Step 1: Find a common denominator for the terms on the left side of the equation. The least common multiple of x and 3x is 3x. (3)/(3x) + (2)/(3x) = (1)/(6) Step 2: Combine the fractions on the left side. (3+2)/(3x) = (1)/(6) (5)/(3x) = (1)/(6) Step 3: Cross-multiply to solve for x. 5 × 6 = 1 × 3x 30 = 3x Step 4: Divide by 3. x = (30)/(3) x = 10 This corresponds to option B. The final answer is B. 10. Question 32: Find the equation whose roots are 2(1)/(2) and (1)/(2). Step 1: Convert the mixed number root to an improper fraction. The roots are = 2(1)/(2) = (5)/(2) and = (1)/(2). Step 2: Calculate the sum of the roots. + = (5)/(2) + (1)/(2) = (6)/(2) = 3 Step 3: Calculate the product of the roots. = (5)/(2) × (1)/(2) = (5)/(4) Step 4: Form the quadratic equation using the formula x^2 - ( + )x + = 0. x^2 - (3)x + (5)/(4) = 0 x^2 - 3x + (5)/(4) = 0 Step 5: Multiply the entire equation by 4 to eliminate the fraction. 4(x^2 - 3x + (5)/(4)) = 4(0) 4x^2 - 12x + 5 = 0 This result does not directly match any of the given options. Self-correction/Assumption: It is common for such multiple-choice questions to have a typo in the provided values if the calculated answer doesn't match any option. If we assume the second root was intended to be 1(1)/(2) (or (3)/(2)) instead of (1)/(2), let's re-evaluate. If = (5)/(2) and = (3)/(2): Sum of roots: + = (5)/(2) + (3)/(2) = (8)/(2) = 4. Product of roots: = (5)/(2) × (3)/(2) = (15)/(4). The equation would be x^2 - 4x + (15)/(4) = 0. Multiplying by 4 gives 4x^2 - 16x + 15 = 0. This matches option C. Given the options, it is highly probable that the second root was intended to be 1(1)/(2). We will proceed with this assumption to select an option. The final answer is C. 4x^2 - 16x + 15 = 0. Question 33: If m = (4b^2)/(xy) + t, express t in terms of m, b, x and y. Step 1: Isolate the term containing t by subtracting (4b^2)/(xy) from both sides of the equation. m - (4b^2)/(xy) = t Step 2: Rewrite the equation with t on the left side. t = m - (4b^2)/(xy) Step 3: Combine the terms on the right side into a single fraction by finding a common denominator, which is xy. t = (m · xy)/(xy) - (4b^2)/(xy) t = (mxy - 4b^2)/(xy) This corresponds to option B. The final answer is B. t = (mxy - 4b^2)/(xy). That's 2 down. 3 left today — send the next one.

A bag contains two black, three green and four red balls. A ball is picked from the bag at random. What is the probability that it is either black or red?

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A bag contains two black, three green and four red balls. A ball is picked from the bag at random. What is the probability that it is either black or red?

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