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.
ScanSolve AI Answer
Step 1: Determine the number of balls of each color. The bag contains a total of 6 balls. Number of red balls = 4. Number of black balls = Total balls - Red balls = 6 - 4 = 2. Step 2: Calculate the probability of drawing two red balls (RR) without replacement. The probability of drawing the first red ball is the number of red balls divided by the total number of balls. P(1st Red) = (4)/(6) After drawing one red ball, there are 3 red balls left and 5 total balls left. The probability of drawing the second red ball is the number of remaining red balls divided by the remaining total balls. P(2nd Red | 1st Red) = (3)/(5) The probability of drawing two red balls is: P(RR) = P(1st Red) × P(2nd Red | 1st Red) = (4)/(6) × (3)/(5) = (12)/(30) = (2)/(5) Step 3: Calculate the probability of drawing two black balls (BB) without replacement. The probability of drawing the first black ball is the number of black balls divided by the total number of balls. P(1st Black) = (2)/(6) After drawing one black ball, there is 1 black ball left and 5 total balls left. The probability of drawing the second black ball is the number of remaining black balls divided by the remaining total balls. P(2nd Black | 1st Black) = (1)/(5) The probability of drawing two black balls is: P(BB) = P(1st Black) × P(2nd Black | 1st Black) = (2)/(6) × (1)/(5) = (2)/(30) = (1)/(15) Step 4: Calculate the total probability of drawing two balls of the same color. The probability of drawing two balls of the same color is the sum of the probabilities of drawing two red balls or two black balls. P(Same Color) = P(RR) + P(BB) P(Same Color) = (2)/(5) + (1)/(15) To add these fractions, find a common denominator, which is 15. P(Same Color) = (2 × 3)/(5 × 3) + (1)/(15) = (6)/(15) + (1)/(15) = (7)/(15) This matches option أ/. The final answer is (7)/(15). Last free one today — make it count tomorrow, or type /upgrade for unlimited.