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: Calculate the probability that both pens drawn are red. There are 5 red pens and 3 blue pens, making a total of 8 pens. The probability of drawing a red pen first is (5)/(8). After drawing one red pen without replacement, there are 4 red pens left and a total of 7 pens remaining. The probability of drawing a second red pen is (4)/(7). The probability of both pens being red is: P(Both red) = (5)/(8) × (4)/(7) = (20)/(56) = (5)/(14) Step 2: Calculate the probability that both pens drawn are blue. The probability of drawing a blue pen first is (3)/(8). After drawing one blue pen without replacement, there are 2 blue pens left and a total of 7 pens remaining. The probability of drawing a second blue pen is (2)/(7). The probability of both pens being blue is: P(Both blue) = (3)/(8) × (2)/(7) = (6)/(56) = (3)/(28) Step 3: Calculate the probability that both pens are of the same color. To find the probability that both pens are of the same color, add the probabilities of both being red and both being blue. P(Same color) = P(Both red) + P(Both blue) P(Same color) = (5)/(14) + (3)/(28) To add these fractions, find a common denominator, which is 28. P(Same color) = (5 × 2)/(14 × 2) + (3)/(28) P(Same color) = (10)/(28) + (3)/(28) P(Same color) = (10 + 3)/(28) = (13)/(28) The probability that both pens are of the same color is (13)/(28). That's 2 down. 3 left today — send the next one.