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
Here's how to calculate the probabilities for drawing fruits. Given: Number of good fruits = 18 Number of bad fruits = 12 Total number of fruits = 18 + 12 = 30 1. Probability that both are good Step 1: Calculate the probability of drawing the first good fruit. P(1st good) = Number of good fruitsTotal number of fruits = (18)/(30) Step 2: Calculate the probability of drawing a second good fruit, given the first was good and not replaced. After drawing one good fruit, there are 17 good fruits left and 29 total fruits. P(2nd good | 1st good) = (17)/(29) Step 3: Calculate the probability that both fruits drawn are good. P(both good) = P(1st good) × P(2nd good | 1st good) P(both good) = (18)/(30) × (17)/(29) P(both good) = (3)/(5) × (17)/(29) P(both good) = (51)/(145) The probability that both fruits are good is (51)/(145). 2. Probability that both are bad Step 1: Calculate the probability of drawing the first bad fruit. P(1st bad) = Number of bad fruitsTotal number of fruits = (12)/(30) Step 2: Calculate the probability of drawing a second bad fruit, given the first was bad and not replaced. After drawing one bad fruit, there are 11 bad fruits left and 29 total fruits. P(2nd bad | 1st bad) = (11)/(29) Step 3: Calculate the probability that both fruits drawn are bad. P(both bad) = P(1st bad) × P(2nd bad | 1st bad) P(both bad) = (12)/(30) × (11)/(29) P(both bad) = (2)/(5) × (11)/(29) P(both bad) = (22)/(145) The probability that both fruits are bad is (22)/(145). Got more? Send 'em.