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
You're on a roll — First, let's count the marbles: • White marbles: 2 • Black marbles: 1 • Gray marbles: 4 • Total marbles: 2 + 1 + 4 = 7 Step 1: Determine the color marble least likely to be drawn. The least likely color is the one with the fewest marbles. There is 1 black marble, 2 white marbles, and 4 gray marbles. The least likely color is black. 1. The color marble least likely to be drawn from the bag is Black. Step 2: Calculate the probability of drawing a black marble. Probability is calculated as Number of favorable outcomesTotal number of outcomes. Number of black marbles = 1 Total marbles = 7 P(Black) = (1)/(7) 2. The probability of drawing a black marble from the bag is (1)/(7). Step 3: Calculate the probability of drawing a gray marble. Number of gray marbles = 4 Total marbles = 7 P(Gray) = (4)/(7) 3. The probability of drawing a gray marble is (4)/(7). Step 4: Calculate the probability of drawing a white marble. Number of white marbles = 2 Total marbles = 7 P(White) = (2)/(7) 4. The probability of drawing a white marble is (2)/(7). Step 5: Calculate the probability of drawing a marble that is not white. Number of marbles that are not white = Number of black marbles + Number of gray marbles = 1 + 4 = 5 Total marbles = 7 P(Not White) = (5)/(7) 5. The probability of drawing a marble that is not white is (5)/(7). Step 6: Compare the likelihood of drawing a marble that is not black versus a marble that is not gray. Number of marbles that are not black = Number of white marbles + Number of gray marbles = 2 + 4 = 6 P(Not Black) = (6)/(7) Number of marbles that are not gray = Number of white marbles + Number of black marbles = 2 + 1 = 3 P(Not Gray) = (3)/(7) Since (6)/(7) > (3)/(7), you would be more likely to draw a marble that is not black. 6. You would be more likely to draw a marble that is not black. This is because there are 6 marbles that are not black (2 white + 4 gray), while there are only 3 marbles that are not gray (2 white + 1 black). Step 7: Calculate the probability of drawing a black marble if three more black marbles were added. Original black marbles = 1 Added black marbles = 3 New number of black marbles = 1 + 3 = 4 Original total marbles = 7 Added marbles = 3 New total marbles = 7 + 3 = 10 P(New Black) = (4)/(10) = (2)/(5) 7. If three more black marbles were added to the bag, the probability of drawing a black marble would be (2)/(5). What's next?