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
Welcome back rosetwumas — missed you this week. Step 1: Determine the total number of pens and the probability of drawing a blue pen first. There are 5 red pens and 3 blue pens. Total number of pens is 5 + 3 = 8. The probability of drawing a blue pen first is the number of blue pens divided by the total number of pens. P(1st pen is blue) = Number of blue pensTotal number of pens = (3)/(8) Step 2: Determine the probability of drawing a second blue pen, given the first was blue and not replaced. After drawing one blue pen, there are now 3 - 1 = 2 blue pens left. The total number of pens remaining is 8 - 1 = 7. The probability of drawing a second blue pen, given the first was blue, is: P(2nd pen is blue | 1st pen is blue) = Number of blue pens remainingTotal number of pens remaining = (2)/(7) Step 3: Calculate the probability that both pens are blue. To find the probability that both pens are blue, multiply the probabilities from Step 1 and Step 2. P(Both pens are blue) = P(1st pen is blue) × P(2nd pen is blue | 1st pen is blue) P(Both pens are blue) = (3)/(8) × (2)/(7) P(Both pens are blue) = (3 × 2)/(8 × 7) P(Both pens are blue) = (6)/(56) Simplify the fraction: P(Both pens are blue) = (3)/(28) The probability that both pens are blue is (3)/(28). Send me the next one 📸