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 probability that both fruits drawn are good. Given: Number of good fruits = 18 Number of bad fruits = 12 Total number of fruits = 18 + 12 = 30 Step 1: Calculate the probability of drawing the first good fruit. The probability of drawing a good fruit on the first draw is the number of good fruits divided by the total number of fruits. 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 now 17 good fruits left and a total of 29 fruits remaining in the bag. P(2nd good | 1st good) = Number of remaining good fruitsTotal remaining fruits = (17)/(29) Step 3: Calculate the probability that both fruits drawn are good. To find the probability that both events occur, multiply the probabilities from Step 1 and Step 2. 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) = (3 × 17)/(5 × 29) P(both good) = (51)/(145) The probability that both fruits are good is (51)/(145). What's next?